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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
##### Keywords:
Peano Arithmetic; Skolem functions; incompleteness
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