Computable axiomatizability of elementary classes

摘要

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 structures. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim