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Comments on is arithmetic finitely consistent?

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is arithmetic finitely consistent?

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i have also asked this question on MSE - https://math.stackexchange.com/questions/4863426/is-arithmetic-finitely-consistent

and reddit - https://www.reddit.com/r/learnmath/comments/1arhu7o/is_arithmetic_finitely_consistent/

no reply , as of the moment i'm writing this post.

Let's take PA1 for example. From godel's 2nd incompleteness theorem, PA1 can't prove its own consistency, more specifically it can't prove that the largest consistent subset of the theory is PA1 itself.

But PA1 has infinite axioms, so can PA1 prove atleast for a given finite set of axioms ( of PA1 ) that they are consistent, specifically that no contradictional proof exists which uses only those axioms ?

Or any formal theory of arithmetic for that matter, can it prove for a finite subset of its own axioms that they are consistent ?

proof logic peano-arithmetic incompletness consistency
posted 9 months ago
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Jason‭
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This was answered in the MathSE post, what is the cross-post policy here? (2 comments)
This was answered in the MathSE post, what is the cross-post policy here?
rmf‭ wrote 9 months ago · edited 9 months ago
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It seems there are differing opinions on:

The FAQ seems to say no to cross-posting, but doesn't specify where it is cross-site or cross-community (e.g. physics and math). I am unsure as to whether the rules on the different (cooking) community affect this community.

Peter Taylor‭ wrote 9 months ago
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The FAQ says "Don't cross-post the same thing in multiple topics". I believe that "topics" is a term which generalises "question" to cover sites which have blog posts, articles, etc. Cross-posting questions across sites / networks without mentioning it is poor netiquette, but here the OP did provide links so people can find the existing answers before starting to work on a new answer. If you think that math.codidact needs a more defined policy then feel free to post on the meta section, which is a more appropriate place for that discussion than these comments.