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arXiv · 1409.1608

Computable Axiomatizability of Elementary Classes

Peter Sinclair
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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 L is an expansion of the language of ordered fields and K is the class of pseudo-o-minimal L-structures (L-structures elementarily equivalent to an ultraproduct of o-minimal structures) then K is not computably axiomatizable. We give a general version of this theorem, and apply it to several classes of topological structures.

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Peter Sinclair. 2014-09-04. Computable Axiomatizability of Elementary Classes. https://doi.org/10.1002/malq.201400110

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