Existentially closed models via constructible sets: There are 2ℵ0 existentially closed pairwise non elementarily equivalent existentially closed ordered groups [Book Review]

Journal of Symbolic Logic 61 (1):277 - 284 (1996)

We prove that there are 2 χ 0 pairwise non elementarily equivalent existentially closed ordered groups, which solve the main open problem in this area (cf. [3, 10]). A simple direct proof is given of the weaker fact that the theory of ordered groups has no model companion; the case of the ordered division rings over a field k is also investigated. Our main result uses constructible sets and can be put in an abstract general framework. Comparison with the standard methods which use forcing (cf. [4]) is sketched
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DOI 10.2307/2275610
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Basic Set Theory.William Mitchell - 1981 - Journal of Symbolic Logic 46 (2):417-419.

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On Nonelementarily Equivalent Pairs of Fields.Anatole Khelif - 2003 - Annals of Pure and Applied Logic 122 (1-3):289-291.

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