## Journal of Symbolic Logic

### Magidor-Malitz Quantifiers in Modules

Andreas Baudisch

#### Abstract

We prove the elimination of Magidor-Malitz quantifiers for $R$-modules relative to certain $Q^2_\alpha$-core sentences and positive primitive formulas. For complete extensions of the elementary theory of $R$-modules it follows that all Ramsey quantifiers ($\aleph_0$-interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no $R$-module having the finite cover property.

#### Article information

Source
J. Symbolic Logic, Volume 49, Issue 1 (1984), 1-8.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741469

Mathematical Reviews number (MathSciNet)
MR736597

Zentralblatt MATH identifier
0584.03023

JSTOR