Which failed attempts have there been to find a contradiction in ZFC or ZF?Nelson's program to show inconsistency of ZFSilver's approach to the inconsistency of $ZFC$Is there a computable model of ZFC?Interpretation of the Second Incompleteness TheoremMartin's Axiom and Determinacy-axioms: independence resultsIf ZFC has a transitive model, does it have one of arbitrary size?A question about sentences in the language of first order ZFC which assert the existence of cardinal numbersWholeness Axiom and Ultimate LIs there a proof (maybe formulated by Feferman) which says that a proof about the (in)consistency of ZFC is unachievable?Silver's approach to the inconsistency of $ZFC$Experiments physically performable in a finite amount of time whose results are independent of ZFCExistence of a model of ZFC in which the natural numbers are really the natural numbers
Which failed attempts have there been to find a contradiction in ZFC or ZF?
Nelson's program to show inconsistency of ZFSilver's approach to the inconsistency of $ZFC$Is there a computable model of ZFC?Interpretation of the Second Incompleteness TheoremMartin's Axiom and Determinacy-axioms: independence resultsIf ZFC has a transitive model, does it have one of arbitrary size?A question about sentences in the language of first order ZFC which assert the existence of cardinal numbersWholeness Axiom and Ultimate LIs there a proof (maybe formulated by Feferman) which says that a proof about the (in)consistency of ZFC is unachievable?Silver's approach to the inconsistency of $ZFC$Experiments physically performable in a finite amount of time whose results are independent of ZFCExistence of a model of ZFC in which the natural numbers are really the natural numbers
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Can you provide any failed attempts to prove that ZF or ZFC to be inconsistent?
References to articles in the literature if there are any will be much appreciated.
Thanks!
set-theory
asked 8 hours ago
AlanAlan
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add a comment |
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Can you provide any failed attempts to prove that ZF or ZFC to be inconsistent?
References to articles in the literature if there are any will be much appreciated.
Thanks!
set-theory
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
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5
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I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago
add a comment |
$begingroup$
Can you provide any failed attempts to prove that ZF or ZFC to be inconsistent?
References to articles in the literature if there are any will be much appreciated.
Thanks!
set-theory
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
$endgroup$
Can you provide any failed attempts to prove that ZF or ZFC to be inconsistent?
References to articles in the literature if there are any will be much appreciated.
Thanks!
set-theory
set-theory
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
asked 8 hours ago
AlanAlan
5984 silver badges14 bronze badges
5984 silver badges14 bronze badges
5
$begingroup$
I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago
add a comment |
5
$begingroup$
I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago
5
5
$begingroup$
I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago
$begingroup$
I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago
add a comment |
1 Answer
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I think the most noticeable one was Nelson's attempt to prove the inconsistency of primitive recursive arithmetic. Terence Tao found a mistake in the proof, but his attempt was posthumously uploaded to arxiv (https://arxiv.org/pdf/1509.09209.pdf), together with an introduction by Sarah Jones Nelson and an afterword by Sam Buss and Terence Tao himself.
Nelson was amongst the very few serious mathematicians who supported the view that arithmetic was indeed inconsistent, based on his ultrafinitist philosophy.
answered 8 hours ago
godeliangodelian
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This might also be relevant mathoverflow.net/questions/36693/…
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– Qfwfq
8 hours ago
add a comment |
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I think the most noticeable one was Nelson's attempt to prove the inconsistency of primitive recursive arithmetic. Terence Tao found a mistake in the proof, but his attempt was posthumously uploaded to arxiv (https://arxiv.org/pdf/1509.09209.pdf), together with an introduction by Sarah Jones Nelson and an afterword by Sam Buss and Terence Tao himself.
Nelson was amongst the very few serious mathematicians who supported the view that arithmetic was indeed inconsistent, based on his ultrafinitist philosophy.
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
$endgroup$
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
$endgroup$
– Qfwfq
8 hours ago
add a comment |
$begingroup$
I think the most noticeable one was Nelson's attempt to prove the inconsistency of primitive recursive arithmetic. Terence Tao found a mistake in the proof, but his attempt was posthumously uploaded to arxiv (https://arxiv.org/pdf/1509.09209.pdf), together with an introduction by Sarah Jones Nelson and an afterword by Sam Buss and Terence Tao himself.
Nelson was amongst the very few serious mathematicians who supported the view that arithmetic was indeed inconsistent, based on his ultrafinitist philosophy.
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
$endgroup$
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
$endgroup$
– Qfwfq
8 hours ago
add a comment |
$begingroup$
I think the most noticeable one was Nelson's attempt to prove the inconsistency of primitive recursive arithmetic. Terence Tao found a mistake in the proof, but his attempt was posthumously uploaded to arxiv (https://arxiv.org/pdf/1509.09209.pdf), together with an introduction by Sarah Jones Nelson and an afterword by Sam Buss and Terence Tao himself.
Nelson was amongst the very few serious mathematicians who supported the view that arithmetic was indeed inconsistent, based on his ultrafinitist philosophy.
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
$endgroup$
I think the most noticeable one was Nelson's attempt to prove the inconsistency of primitive recursive arithmetic. Terence Tao found a mistake in the proof, but his attempt was posthumously uploaded to arxiv (https://arxiv.org/pdf/1509.09209.pdf), together with an introduction by Sarah Jones Nelson and an afterword by Sam Buss and Terence Tao himself.
Nelson was amongst the very few serious mathematicians who supported the view that arithmetic was indeed inconsistent, based on his ultrafinitist philosophy.
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
answered 8 hours ago
godeliangodelian
2,5791 gold badge22 silver badges23 bronze badges
2,5791 gold badge22 silver badges23 bronze badges
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
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– Qfwfq
8 hours ago
add a comment |
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
$endgroup$
– Qfwfq
8 hours ago
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
$endgroup$
– Qfwfq
8 hours ago
$begingroup$
This might also be relevant mathoverflow.net/questions/36693/…
$endgroup$
– Qfwfq
8 hours ago
add a comment |
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I assume you want attempts by competent mathematicians (not cranks). Competent set theorists who doubt the consistency of ZFC are rare, and ones who have seriously sought a contradiction are even rarer. The only example that comes to mind is Jack Silver, who didn't publish failed attempts, but did publish a lot of good set theory arising from those attempts. See mathoverflow.net/questions/260944 for a little information about that.
$endgroup$
– Andreas Blass
8 hours ago