Computable axiomatizability of elementary classes. Issue 1 (19th January 2016)

• Record Type: Journal Article
• Authors: Sinclair, Peter
• Is Part Of: Mathematical logic quarterly. Volume 62:Issue 1/2(2016)
• Page Start: 46
• Page End: 51
• Publication Date: 2016-01-19
• Subjects: Mathematics -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1002/malq.201400110
• Languages: English
• ISSNs: 0942-5616

Abstract

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.