Quantifier elimination for neocompact sets

Journal of Symbolic Logic 63 (4):1442-1472 (1998)
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Abstract

We shall prove quantifier elimination theorems for neocompact formulas, which define neocompact sets and are built from atomic formulas using finite disjunctions, infinite conjunctions, existential quantifiers, and bounded universal quantifiers. The neocompact sets were first introduced to provide an easy alternative to nonstandard methods of proving existence theorems in probability theory, where they behave like compact sets. The quantifier elimination theorems in this paper can be applied in a general setting to show that the family of neocompact sets is countably compact. To provide the necessary setting we introduce the notion of a law structure. This notion was motivated by the probability law of a random variable. However, in this paper we discuss a variety of model theoretic examples of the notion in the light of our quantifier elimination results

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References found in this work

A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.
General Topology.John L. Kelley - 1962 - Journal of Symbolic Logic 27 (2):235-235.
From discrete to continuous time.H. Jerome Keisler - 1991 - Annals of Pure and Applied Logic 52 (1-2):99-141.

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