Three concepts of ordinal numbers are examined with a view to their intuitiveriess and existence in two principle systems of axiomatic set theory. The first is based on equivalence classes of the similarity relation between well-ordered sets. Two alternatives are suggested in later chapters for overcoming the problems arizing from this definition. Next, ordinal numbers are defined as certain representatives of these equivalence classes,, and one of several such possible definitions is taken for proving the fundamental properties of these ordinals. Finally, a generalization of Peano's axioms provides us with a method of defining ordinal numbers which are the ultimate result of abstractions. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis explores the fundamental properties of the contingent.

The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.

"The purpose of this paper is to record the results of a study of an abstract set upon which a distance function, having certain properties, has been defined. It is assumed that the reader is familiar with the fundamental concepts of set theory"--Introduction. / "June, 1959." / Typescript. / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: H. C. Griffith, Professor Directing Paper. / Includes bibliographical references (leaf 26).

"This paper is concerned with systems of distinct representatives (abbreviated by S.D.R.) and related combinatorial topics"--Introduction. / Typescript. / "August, 1959." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Marion F. Tinsley, Professor Directing Paper. / Includes bibliographical references (leaf 25).

We give some background on the free part of the action of tuples of integers into 2. We will construct specific structures on this space, and then show that certain other structures cannot exist.

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