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A note on definable Skolem functions. (English) Zbl 0754.03021
The author’s main observation is that Peano Arithmetic (PA) is an example of a first-order theory that has definable Skolem functions and is not model-complete. In order to show that PA has these properties he has to use the incompleteness of PA. He might have mentioned the complete theory of the structure \(\langle \mathbb{N},<\rangle\) as an easier example of a first-order theory with the required properties.
MSC:
03C07 Basic properties of first-order languages and structures
03F30 First-order arithmetic and fragments
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