Revisions to A “formalistic” variant of the Gödel completeness theorem

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edited Apr 1, 2018 at 14:45

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And if somebody could give me a reference to this statement (with a proof), this, I believe, will be a proper solution to what I need. Does anybody know such a reference?

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edited Apr 1, 2018 at 14:27

Sergei Akbarov

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I believe this is more or less equivalent to what Matt F.F suggests in his answer:

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edited Apr 1, 2018 at 14:17

Sergei Akbarov

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EDIT 01.04.2018. Recently one of my friends showed me an article by K.Smorynski in Handbook of Mathematical Logic (edited by Jon Barwise) where he formulates a statement which he calls "the Hilbert-Bernays theorem" (Theorem 6.1.1 in volume 4) and which as far as I understand is equivalent to the following:

If a formal theory $T$ is consistent then it has an interpretation in PA.

I believe this is more or less equivalent to what Matt.F suggests in his answer:

If a formal theory $T$ is consistent then it has an interpretation in MK.

And if somebody could give me a reference to this statement, this, I believe, will be a proper solution to what I need. Does anybody know such a reference?