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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The axiom of choice, fixed point theorems, and inductive ordered sets


Author: Milan R. Tasković
Journal: Proc. Amer. Math. Soc. 116 (1992), 897-904
MSC: Primary 04A25; Secondary 06A06
DOI: https://doi.org/10.1090/S0002-9939-1992-1111224-8
MathSciNet review: 1111224
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Abstract: This paper continues the study of the inductiveness of posets in terms of fixed apexes and points. The author proves some new equivalents of the Axiom of Choice, i.e., Zorn's lemma. These statements are of fixed apex type and fixed point type theorems. The paper includes comments about these theorems and presents new characterizations of inductiveness and quasi-inductiveness of posets in terms of fixed apexes and fixed points.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1111224-8
Keywords: Inductive partially ordered sets, Axiom of Choice, Zorn's lemma, fixed apexes, fixed points
Article copyright: © Copyright 1992 American Mathematical Society