Fixed point theorems of the mappings of partially ordered sets
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In this paper without using any of the equivalent statements of the Axiom of Choice we give a short proof of the Fixed Point Theorems 1 and 2, and, via a simple derivation of Zorn’s Lemma from the Axiom of Choice (see Theorem 3) we prove Fixed Point Theorem 4.
KeywordsPoint Theorem Equivalent Statement Maximal Element Distinct Element Initial Segment
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