van den Dries, Lou Algebraic theories with definable Skolem functions. (English) Zbl 0596.03032 J. Symb. Log. 49, 625-629 (1984). 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. Cited in 2 ReviewsCited in 25 Documents MSC: 03C60 Model-theoretic algebra Keywords:real closed fields; definitional extension with built-in Skolem functions; p-adically closed fields PDF BibTeX XML Cite \textit{L. van den Dries}, J. Symb. Log. 49, 625--629 (1984; Zbl 0596.03032) Full Text: DOI References: [1] Une théorie de Galois imaginaire 48 pp 1151– (1983) [2] On definable subsets of p-adic fields 41 pp 605– (1976) [3] Defining algebraic elements 38 pp 93– (1973) [4] DOI: 10.1007/BF01218373 · Zbl 0445.16020 · doi:10.1007/BF01218373 [5] Model theory (1973) [6] DOI: 10.1090/pspum/012/0257030 · doi:10.1090/pspum/012/0257030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.