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On the foundations of the theory of ordinal numbers Dunik, Peter Anthony

Abstract

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.

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