Ramsey quantifiers and the finite cover property

John Theodore Baldwin and David William Kueker

Vol. 90 (1980), No. 1, 11–19

DOI: 10.2140/pjm.1980.90.11

Abstract

The main results of this paper are the following Theorem A. The Magidor-Malitz quantifier (in the ℵ₀-interpretation) is eliminable from a countable stable theory T if and only if T does not have the finite cover property. Theorem B. There is an ℵ₀-categorical theory which is not finitely model complete.

Mathematical Subject Classification 2000

Primary: 03C80

Secondary: 03C10, 03C45

Milestones

Received: 18 May 1979

Revised: 23 July 1979

Published: 1 September 1980