Axiom of Choice Equivalences and Some Applications
Description:
In this paper several equivalences of the axiom of choice are examined. In particular, the axiom of choice, Zorn's lemma, Tukey's lemma, the Hausdorff maximal principle, and the well-ordering theorem are shown to be equivalent. Cardinal and ordinal number theory is also studied. The Schroder-Bernstein theorem is proven and used in establishing order results for cardinal numbers. It is also demonstrated that the first uncountable ordinal space is unique up to order isomorphism. We conclude by en…
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Date:
August 1983
Creator:
Race, Denise T. (Denise Tatsch)
Partner:
UNT Libraries