A simple and elementary proof of Zorn’s Lemma | [Discrete Mathematics Letters • 2024]

Author(s):

1. Koji Nuida: Institute of Mathematics for Industry, Kyushu University,Fukuoka,Japan

Abstract:

Zorn's Lemma is a well-known equivalent of the Axiom of Choice. It is usually regarded as a topic in axiomatic set theory, and its historically standard proof (from the Axiom of Choice) relies on transfinite recursion, a non-elementary set-theoretic concept. However, the statement of Zorn's Lemma itself uses only elementary terminology of partially ordered sets. Hence, it is worthy to establish a proof using only such elementary terminology. Following this line of study, a new simple proof of Zorn's Lemma is given that does not even use the notion of a well-ordered set.

Page(s): 108-110

DOI: 10.47443/dml.2023.143

Published: Journal: Discrete Mathematics Letters, Volume: 13, Issue: 0, Year: 2024

Keywords:

partially ordered sets , Zorns Lemma , elementary proof

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