Computable axiomatizability of elementary classes

Mathematical Logic Quarterly 62 (1-2):46-51 (2016)
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Abstract

The goal of this paper is to generalise Alex Rennet's proof of the non‐axiomatizability of the class of pseudo‐o‐minimal structures. Rennet showed that if is an expansion of the language of ordered fields and is the class of pseudo‐o‐minimal ‐structures (‐structures elementarily equivalent to an ultraproduct of o‐minimal structures) then is not computably axiomatizable. We give a general version of this theorem, and apply it to several classes of structures.

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10.1002/malq.201400110

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References found in this work

Cell decompositions of C-minimal structures.Deirdre Haskell & Dugald Macpherson - 1994 - Annals of Pure and Applied Logic 66 (2):113-162.
A version of o-minimality for the p-adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
First order topological structures and theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.
O-minimalism.Hans Schoutens - 2014 - Journal of Symbolic Logic 79 (2):355-409.

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