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UBC Theses and Dissertations

Postulational methods Stallard, Samuel Ernest

Abstract

Since the middle of the 19th century there has been a rapid growth in the use of the postulational method in mathematics. Concurrently with this growth such concepts have arisen as the consistency, independence or completeness of abstract sets of postulates. The definitions of these concepts, as well as the methods used to test postulates for these properties, are widely scattered throughout mathematical and logical, literature. The object of this thesis has been to make a survey of this new field (which we might call Axiomatics) and to indicate some of the techniques used in it. The method has been to take a simple set of postulates (those for the relation of serial order) and then devise proofs for the consistency, completeness, etc. of these postulates. Each proof illustrating one of the methods currently in use for testing postulates.

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