Simple book on model theoryCategory theory and model theory as “natural” counterpartsIs it necessary that model of theory is a set?Incompleteness and nonstandard models of arithmeticHow to think like a set (or a model) theorist.A book about model theoryConstructible models of New Foundations?Are there textbooks on logic where the references to set theory appear only after the construction of set theory?What “metatheory” did early set theory/logic researchers use to prove semantic results?
Simple book on model theory
Category theory and model theory as “natural” counterpartsIs it necessary that model of theory is a set?Incompleteness and nonstandard models of arithmeticHow to think like a set (or a model) theorist.A book about model theoryConstructible models of New Foundations?Are there textbooks on logic where the references to set theory appear only after the construction of set theory?What “metatheory” did early set theory/logic researchers use to prove semantic results?
$begingroup$
I was expressed by how Mendelson describes models in his Introduction to mathematical logic. Now I am looking for a simple and concrete model theory guide. The book (video source, etc.) must:
- Include the concrete methods with their proofs and must answer the following questions:
1.1. how to know if a theory has a model
1.2. how to build a model if a theory is consistent
1.3. how to know if a class of structures forms the models of some theory
1.4. how to build a theory for an elementary class
1.5. given a structure, what information can be obtained by logic - Be concentrated on finite models and theories (that's why I didn't like Keisler with his ordinals and cardinals)
- Not contain too much algebra (that's why I didn't like Marker with his p-adic numbers and fields extensions)
- Not contain complexity theory at all (that's why I didn't like Ebbinghaus)
That's why I am interested in a simple and concrete model guide (with proofs). If there is no such a book, is it real to discover the methods above by myself?
reference-request lo.logic model-theory textbook-recommendation universal-algebra
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I was expressed by how Mendelson describes models in his Introduction to mathematical logic. Now I am looking for a simple and concrete model theory guide. The book (video source, etc.) must:
- Include the concrete methods with their proofs and must answer the following questions:
1.1. how to know if a theory has a model
1.2. how to build a model if a theory is consistent
1.3. how to know if a class of structures forms the models of some theory
1.4. how to build a theory for an elementary class
1.5. given a structure, what information can be obtained by logic - Be concentrated on finite models and theories (that's why I didn't like Keisler with his ordinals and cardinals)
- Not contain too much algebra (that's why I didn't like Marker with his p-adic numbers and fields extensions)
- Not contain complexity theory at all (that's why I didn't like Ebbinghaus)
That's why I am interested in a simple and concrete model guide (with proofs). If there is no such a book, is it real to discover the methods above by myself?
reference-request lo.logic model-theory textbook-recommendation universal-algebra
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
4
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago
add a comment |
$begingroup$
I was expressed by how Mendelson describes models in his Introduction to mathematical logic. Now I am looking for a simple and concrete model theory guide. The book (video source, etc.) must:
- Include the concrete methods with their proofs and must answer the following questions:
1.1. how to know if a theory has a model
1.2. how to build a model if a theory is consistent
1.3. how to know if a class of structures forms the models of some theory
1.4. how to build a theory for an elementary class
1.5. given a structure, what information can be obtained by logic - Be concentrated on finite models and theories (that's why I didn't like Keisler with his ordinals and cardinals)
- Not contain too much algebra (that's why I didn't like Marker with his p-adic numbers and fields extensions)
- Not contain complexity theory at all (that's why I didn't like Ebbinghaus)
That's why I am interested in a simple and concrete model guide (with proofs). If there is no such a book, is it real to discover the methods above by myself?
reference-request lo.logic model-theory textbook-recommendation universal-algebra
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I was expressed by how Mendelson describes models in his Introduction to mathematical logic. Now I am looking for a simple and concrete model theory guide. The book (video source, etc.) must:
- Include the concrete methods with their proofs and must answer the following questions:
1.1. how to know if a theory has a model
1.2. how to build a model if a theory is consistent
1.3. how to know if a class of structures forms the models of some theory
1.4. how to build a theory for an elementary class
1.5. given a structure, what information can be obtained by logic - Be concentrated on finite models and theories (that's why I didn't like Keisler with his ordinals and cardinals)
- Not contain too much algebra (that's why I didn't like Marker with his p-adic numbers and fields extensions)
- Not contain complexity theory at all (that's why I didn't like Ebbinghaus)
That's why I am interested in a simple and concrete model guide (with proofs). If there is no such a book, is it real to discover the methods above by myself?
reference-request lo.logic model-theory textbook-recommendation universal-algebra
reference-request lo.logic model-theory textbook-recommendation universal-algebra
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
edited 13 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
3,5953 gold badges24 silver badges34 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
asked 14 hours ago
Elmar GuseinovElmar Guseinov
242 bronze badges
242 bronze badges
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Elmar Guseinov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
4
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago
add a comment |
4
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago
4
4
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
2
2
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The best book for you is probably A Shorter Model Theory by Hodges.
Some comments on your question, though: First, you should be aware that the model theory of finite structures and the model theory of infinite structures have extremely different characters - so much so that finite model theory is essentially a separate subfield of logic, which is much closer to computer science and complexity theory. This can be (partially) explained by the fact that first-order logic is powerful enough to completely describe finite structures, so interesting questions in the first-order model theory of finite structures have to impose some constraints: working with fragments of first-order logic and taking complexity into account.
If you're really interested in finite model theory, you can take a look at this question, which has some references in the comments and answers. To my knowledge, the book by Ebbinghaus and Flum is the textbook on the subject which contains the least complexity theory (though there are probably books that I'm not aware of).
On the other hand, "ordinary" model theory is primarily concerned with infinite models, and as a result it's hard to avoid some set theory creeping in. If you're really turned off by ordinals and cardinals, I would recommend: (1) learn something about them, set theory is a beautiful subject! (2) in the mean time, concentrate on the model theory of countably infinite structures. This is a domain in which you get to see many of the concepts and techniques of model theory at work without any transfinite inductions in sight.
It's also the case that most of the interesting examples in model theory come from algebra. So it's hard to achieve your requirements 2, 3, and 4. But this is why I suggested Hodges: In my experience students without a strong background in algebra and set theory find Hodges's book to be easier to read than Marker's.
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
$endgroup$
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
I offer you to try these books too:
-A Guide to Classical and Modern Model Theory, Written by Annaliza Marcja and Carlo Toffalori. I could find many tangible examples in this book when I was trying to understand Marker's.
-A course in Model Theory, Katrin Tent and Martin Ziegler. Although one can find most of the chapters in Marker's book, but some chapters are written more simple seemingly.
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The best book for you is probably A Shorter Model Theory by Hodges.
Some comments on your question, though: First, you should be aware that the model theory of finite structures and the model theory of infinite structures have extremely different characters - so much so that finite model theory is essentially a separate subfield of logic, which is much closer to computer science and complexity theory. This can be (partially) explained by the fact that first-order logic is powerful enough to completely describe finite structures, so interesting questions in the first-order model theory of finite structures have to impose some constraints: working with fragments of first-order logic and taking complexity into account.
If you're really interested in finite model theory, you can take a look at this question, which has some references in the comments and answers. To my knowledge, the book by Ebbinghaus and Flum is the textbook on the subject which contains the least complexity theory (though there are probably books that I'm not aware of).
On the other hand, "ordinary" model theory is primarily concerned with infinite models, and as a result it's hard to avoid some set theory creeping in. If you're really turned off by ordinals and cardinals, I would recommend: (1) learn something about them, set theory is a beautiful subject! (2) in the mean time, concentrate on the model theory of countably infinite structures. This is a domain in which you get to see many of the concepts and techniques of model theory at work without any transfinite inductions in sight.
It's also the case that most of the interesting examples in model theory come from algebra. So it's hard to achieve your requirements 2, 3, and 4. But this is why I suggested Hodges: In my experience students without a strong background in algebra and set theory find Hodges's book to be easier to read than Marker's.
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
$endgroup$
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
The best book for you is probably A Shorter Model Theory by Hodges.
Some comments on your question, though: First, you should be aware that the model theory of finite structures and the model theory of infinite structures have extremely different characters - so much so that finite model theory is essentially a separate subfield of logic, which is much closer to computer science and complexity theory. This can be (partially) explained by the fact that first-order logic is powerful enough to completely describe finite structures, so interesting questions in the first-order model theory of finite structures have to impose some constraints: working with fragments of first-order logic and taking complexity into account.
If you're really interested in finite model theory, you can take a look at this question, which has some references in the comments and answers. To my knowledge, the book by Ebbinghaus and Flum is the textbook on the subject which contains the least complexity theory (though there are probably books that I'm not aware of).
On the other hand, "ordinary" model theory is primarily concerned with infinite models, and as a result it's hard to avoid some set theory creeping in. If you're really turned off by ordinals and cardinals, I would recommend: (1) learn something about them, set theory is a beautiful subject! (2) in the mean time, concentrate on the model theory of countably infinite structures. This is a domain in which you get to see many of the concepts and techniques of model theory at work without any transfinite inductions in sight.
It's also the case that most of the interesting examples in model theory come from algebra. So it's hard to achieve your requirements 2, 3, and 4. But this is why I suggested Hodges: In my experience students without a strong background in algebra and set theory find Hodges's book to be easier to read than Marker's.
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
$endgroup$
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
The best book for you is probably A Shorter Model Theory by Hodges.
Some comments on your question, though: First, you should be aware that the model theory of finite structures and the model theory of infinite structures have extremely different characters - so much so that finite model theory is essentially a separate subfield of logic, which is much closer to computer science and complexity theory. This can be (partially) explained by the fact that first-order logic is powerful enough to completely describe finite structures, so interesting questions in the first-order model theory of finite structures have to impose some constraints: working with fragments of first-order logic and taking complexity into account.
If you're really interested in finite model theory, you can take a look at this question, which has some references in the comments and answers. To my knowledge, the book by Ebbinghaus and Flum is the textbook on the subject which contains the least complexity theory (though there are probably books that I'm not aware of).
On the other hand, "ordinary" model theory is primarily concerned with infinite models, and as a result it's hard to avoid some set theory creeping in. If you're really turned off by ordinals and cardinals, I would recommend: (1) learn something about them, set theory is a beautiful subject! (2) in the mean time, concentrate on the model theory of countably infinite structures. This is a domain in which you get to see many of the concepts and techniques of model theory at work without any transfinite inductions in sight.
It's also the case that most of the interesting examples in model theory come from algebra. So it's hard to achieve your requirements 2, 3, and 4. But this is why I suggested Hodges: In my experience students without a strong background in algebra and set theory find Hodges's book to be easier to read than Marker's.
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
$endgroup$
The best book for you is probably A Shorter Model Theory by Hodges.
Some comments on your question, though: First, you should be aware that the model theory of finite structures and the model theory of infinite structures have extremely different characters - so much so that finite model theory is essentially a separate subfield of logic, which is much closer to computer science and complexity theory. This can be (partially) explained by the fact that first-order logic is powerful enough to completely describe finite structures, so interesting questions in the first-order model theory of finite structures have to impose some constraints: working with fragments of first-order logic and taking complexity into account.
If you're really interested in finite model theory, you can take a look at this question, which has some references in the comments and answers. To my knowledge, the book by Ebbinghaus and Flum is the textbook on the subject which contains the least complexity theory (though there are probably books that I'm not aware of).
On the other hand, "ordinary" model theory is primarily concerned with infinite models, and as a result it's hard to avoid some set theory creeping in. If you're really turned off by ordinals and cardinals, I would recommend: (1) learn something about them, set theory is a beautiful subject! (2) in the mean time, concentrate on the model theory of countably infinite structures. This is a domain in which you get to see many of the concepts and techniques of model theory at work without any transfinite inductions in sight.
It's also the case that most of the interesting examples in model theory come from algebra. So it's hard to achieve your requirements 2, 3, and 4. But this is why I suggested Hodges: In my experience students without a strong background in algebra and set theory find Hodges's book to be easier to read than Marker's.
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
edited 4 hours ago
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
answered 8 hours ago
Alex KruckmanAlex Kruckman
2,1291 gold badge12 silver badges16 bronze badges
2,1291 gold badge12 silver badges16 bronze badges
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
Thanks a lot! The idea about countable sets seems to be useful for me. Actually, I am working with graphs and looking for new methods.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
I think that the following idea is very useful for graphs. Assume we want to prove that all objects O have some property P. Then we can try to prove that a theory T for O axiomatizes the same class as T+P. Or we can try to prove that O+(-P) is inconsistent.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
I offer you to try these books too:
-A Guide to Classical and Modern Model Theory, Written by Annaliza Marcja and Carlo Toffalori. I could find many tangible examples in this book when I was trying to understand Marker's.
-A course in Model Theory, Katrin Tent and Martin Ziegler. Although one can find most of the chapters in Marker's book, but some chapters are written more simple seemingly.
edited 10 hours ago
Martin Sleziak
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answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
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Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
I offer you to try these books too:
-A Guide to Classical and Modern Model Theory, Written by Annaliza Marcja and Carlo Toffalori. I could find many tangible examples in this book when I was trying to understand Marker's.
-A course in Model Theory, Katrin Tent and Martin Ziegler. Although one can find most of the chapters in Marker's book, but some chapters are written more simple seemingly.
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
I offer you to try these books too:
-A Guide to Classical and Modern Model Theory, Written by Annaliza Marcja and Carlo Toffalori. I could find many tangible examples in this book when I was trying to understand Marker's.
-A course in Model Theory, Katrin Tent and Martin Ziegler. Although one can find most of the chapters in Marker's book, but some chapters are written more simple seemingly.
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I offer you to try these books too:
-A Guide to Classical and Modern Model Theory, Written by Annaliza Marcja and Carlo Toffalori. I could find many tangible examples in this book when I was trying to understand Marker's.
-A course in Model Theory, Katrin Tent and Martin Ziegler. Although one can find most of the chapters in Marker's book, but some chapters are written more simple seemingly.
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
edited 10 hours ago
Martin Sleziak
3,5953 gold badges24 silver badges34 bronze badges
3,5953 gold badges24 silver badges34 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
answered 11 hours ago
Maryam AjorlouMaryam Ajorlou
365 bronze badges
365 bronze badges
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Maryam Ajorlou is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
Thanks a lot! I will try to learn these books.
$endgroup$
– Elmar Guseinov
11 hours ago
2
2
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
I especially like the book by Tent and Ziegler (which in its second half goes far beyond the material in Marker's book). But I don't think it's suitable as a first introduction to model theory - it's very terse, and there are few examples.
$endgroup$
– Alex Kruckman
8 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
$begingroup$
Oh, I can't find it but it seems to be interesting.
$endgroup$
– Elmar Guseinov
6 hours ago
add a comment |
Elmar Guseinov is a new contributor. Be nice, and check out our Code of Conduct.
Elmar Guseinov is a new contributor. Be nice, and check out our Code of Conduct.
Elmar Guseinov is a new contributor. Be nice, and check out our Code of Conduct.
Elmar Guseinov is a new contributor. Be nice, and check out our Code of Conduct.
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4
$begingroup$
Concerning a few of your criteria: 1.1. It is algorithmically undecidable whether a theory (or even a single sentence) has a model. 1.2. A theory that has models need not have computable models. 2 It is algorithmically undecidable whether a theory (or even a single sentence) has a finite model. (My opinion about 4: Finite model theory and complexity theory are nearly the same thing.) In other words, model theory is neither as simple nor as isolated from other fields as you want it to be.
$endgroup$
– Andreas Blass
12 hours ago
$begingroup$
Thanks for your answer! Actually, I realize the difficulties you've mentioned. I think I want to learn about special (computable) cases and methods of the model-building.
$endgroup$
– Elmar Guseinov
11 hours ago
2
$begingroup$
In a finite language any collection of finite structures is the class of finite models of some theory.
$endgroup$
– James Hanson
11 hours ago
$begingroup$
Thank you! It is very interesting. I didn't know it.
$endgroup$
– Elmar Guseinov
11 hours ago
$begingroup$
I suppose this is because we can describe a finite structure with a formula which has exactly this structure as a model.
$endgroup$
– Elmar Guseinov
10 hours ago