Timeline for Does PA+Con(PA) entail the existence of non-standard models of PA?

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Apr 2, 2015 at 1:47	comment	added	Noah Schweber		Isn't that the usual statement of Tennenbaum's theorem?
Apr 1, 2015 at 20:50	comment	added	stan		To show that $RCA_{0}+Con(RCA_{0})$ cannot prove that $RCA_{0}$ has nonstandard models, do we need Tennenbaum's theorem as usually stated, or just the fact that nonstandard models code non-recursive sets?
Mar 23, 2015 at 12:25	comment	added	Joel David Hamkins		Once PA knows that the theory $\text{PA}^*$ is consistent, then it can define the Henkin model, since that is arithmetically definable in PA. That is, we may define in PA a (class) domain of objects and functions $+$ and $\cdot$ on them and an interpretation for $0$ and $1$ and $c$, so that the resulting class is a nonstandard model of PA. So this is a sense in which PA may talk about the models directly.
Mar 23, 2015 at 7:56	vote	accept	stan
Mar 23, 2015 at 4:08	history	edited	Noah Schweber	CC BY-SA 3.0	added 188 characters in body
Mar 23, 2015 at 4:00	history	answered	Noah Schweber	CC BY-SA 3.0