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Correct subject/verb agreements
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edit approved Jul 23, 2020 at 23:35
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edit approved Jul 23, 2020 at 23:35
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AreIs there any proofsa proof of Secondthe second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I

I came across a short proof by Thomas Jech (here), but iI think he uses Godel numbering for defining "k" in his proof. Nevertheless Nevertheless Bagaria in his article (here) in referencing JeshJech, mentioned itthere is no need of arithmetizing the syntax. My

My question is, does his proof crucially dependsdepend on Godel numbering? If the answer is yes, is there any proofsa proof of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

Are there any proofs of Second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas Jech (here), but i think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jesh, mentioned it is no need of arithmetizing the syntax. My question is, does his proof crucially depends on Godel numbering? If the answer is yes, is there any proofs of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

Is there a proof of the second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)?

I came across a short proof by Thomas Jech (here), but I think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jech, mentioned there is no need of arithmetizing the syntax.

My question is, does his proof crucially depend on Godel numbering? If the answer is yes, is there a proof of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

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Ali
Ali
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Are there any proofs of Second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas Jech (here), but i think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jesh, mentioned it is no need of arithmetizing the syntax. My question is, does his proof crucially depends on Godel numbering? If the ansereanswer is yes, is there any proofs of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

Are there any proofs of Second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas Jech (here), but i think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jesh, mentioned it is no need of arithmetizing the syntax. My question is, does his proof crucially depends on Godel numbering? If the ansere is yes, is there any proofs of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

Are there any proofs of Second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas Jech (here), but i think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jesh, mentioned it is no need of arithmetizing the syntax. My question is, does his proof crucially depends on Godel numbering? If the answer is yes, is there any proofs of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?

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Ali
Ali
  • 103
  • 4

Proof of second incompleteness theorem for Set theory without Arithmetization of Syntax

Are there any proofs of Second incompleteness theorem of Godel for set theory which doesn't use Arithmetization of Syntax (Godel numbering)? I came across a short proof by Thomas Jech (here), but i think he uses Godel numbering for defining "k" in his proof. Nevertheless Bagaria in his article (here) in referencing Jesh, mentioned it is no need of arithmetizing the syntax. My question is, does his proof crucially depends on Godel numbering? If the ansere is yes, is there any proofs of second incompleteness theorem for Set theory(ZFC) which doesn't need some fixed coding of formulas by proving there is no model of ZFC, in ZFC itself?, or the use of such coding is unavoidable?