On the Boolean algebras of definable sets in weakly o-minimal theories

✍ Scribed by Stefano Leonesi; Carlo Toffalori

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 141 KB
• Volume: 50
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200310095

✦ Synopsis

Abstract

We consider the sets definable in the countable models of a weakly o‐minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic (hence T is p‐ω‐categorical), in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete (convex) subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within expansions of Boolean lattices, every weakly o‐minimal theory is p‐ω‐categorical. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)