Date

1967

Document Type

Thesis

Degree

Master of Science

Department

Mathematics

First Adviser

Hailperin, Theodore

Abstract

This paper presents a review of the literature on applications of the Completeness Theorem, presented within the framework of arithmetical classes. Generalized methods of application are first offered; a new result is introduced which simplifies many of the examples appearing in the literature. Applications to group theory, Boolean algebra, and set theory are then considered, with special consideration given to the relationship between the Completeness Theorem and the Axiom of Choice.

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