Computable axiomatizability of elementary classes. Issue 1 (19th January 2016) - Sinclair, Peter
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 structures.