Timeline for Tarski's Theorem and Gödel's Second Incompleteness Theorem

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Nov 17, 2012 at 19:23	comment	added	Sridhar Ramesh		Well, one caveat: One needs that Tarski's result is constructive enough that we have not just "For every T, for every model, there is a G such that...", but in fact "For every T, there is a G such that for every model...". But, basically, were Tarski's result phrased as strongly as its proof actually warranted, it would give us everything.
Nov 17, 2012 at 18:54	comment	added	Sridhar Ramesh		I've modified the word of the second paragraph to alleviate this concern. The second incompleteness theorem follows from the simultaneous "external" and "internal" truth of Tarski's theorem (by which I mean, the fact that Tarski's theorem is both true and provable (or, just as well, true inside every model)).
Nov 17, 2012 at 18:45	history	edited	Sridhar Ramesh	CC BY-SA 3.0	added 56 characters in body
Nov 17, 2012 at 16:49	comment	added	provocateur		But all that really shows is that some of the ideas used in Tarski's result are also used in a proof of the 2nd incompleteness theorem, which is a pretty modest claim. The question, I take it, is rather whether given the truth of Tarski's theorem, the truth of the 2nd incompleteness theorem follows by some clever argument or other.
Nov 17, 2012 at 5:14	history	edited	Sridhar Ramesh	CC BY-SA 3.0	added 67 characters in body; added 32 characters in body
Nov 17, 2012 at 5:08	history	answered	Sridhar Ramesh	CC BY-SA 3.0