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Algebraic theories with definable Skolem functions. (English) Zbl 0596.03032
A well-known example of a theory with built-in Skolem functions is first- order Peano arithmetic. The theory of real closed fields has a definitional extension with built-in Skolem functions. Let us say that a theory has definable Skolem functions if it has a definitional extension with built-in Skolem functions. Let T admit quantifier elimination. Then T has definable Skolem functions if and only if each model A of $$T_{\forall}$$ has an extension $$A_ 1$$ which is algebraic over A and rigid over A. The theory of p-adically closed fields has definable Skolem functions.

##### MSC:
 03C60 Model-theoretic algebra
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##### References:
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