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Classification Theory and Stationary Logic

Published online by Cambridge University Press:  20 November 2018

Alan H. Mekler
Alan H. Mekler*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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Stationary logic L(aa) is obtained for Lωω by adding a quantifier aa which ranges over countable sets and is interpreted to mean “for a closed unbounded set of countable subsets”. The dual quantifier for aa is stat, i.e., stat sφ(s) is equivalent to ¬aa s ¬φ(s). In the study of the L(aa)-model theory of structures a particular well behaved class was isolated, the finitely determinate structures. These are structures in which the quantifier “stat” can be replaced by the quantifier “aa” without changing the validity of sentences. Many structures such as R and all ordinals are finitely determinate. In this paper we will be concerned with finitely determinate first order theories, i.e., those theories all of whose models are finitely determinate.

Example 0.1. [5] The theory of dense linear orderings is not finitely determinate. Let S be a stationary costationary subset of ω1 and

where

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 4 , 01 August 1987 , pp. 893 - 907
Copyright
Copyright © Canadian Mathematical Society 1987

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