A Model–Theoretic Approach to Proof Theory by Henryk Kotlarski

Author:Henryk Kotlarski
Language: eng
Format: epub
ISBN: 9783030289218
Publisher: Springer International Publishing

Lemma 3.1.4

If is a formula and then

Proof

The thesis follows from the fact that .

We shall prove later that no –extension is elementary (in contrast with “ordinary” end–extensions) and that each such extension is proper, this will follow from the proof of Tarski’s theorem, i.e., Theorem 3.2.7.

It should be noticed that iterations of the construction of a model by means of the arithmetized completeness theorem give nothing essentially new. The model of the form has an elementary submodel of the form . Let us be more precise here.

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