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Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis
Author(s) -
Rubin Arthur L.,
Rubin Jean E.
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390104
Subject(s) - axiom independence , axiom of choice , mathematics , trichotomy (philosophy) , zermelo–fraenkel set theory , constructive set theory , continuum hypothesis , axiom , urelement , partition (number theory) , mathematical economics , calculus (dental) , epistemology , mathematical analysis , combinatorics , computer science , geometry , set theory , philosophy , set (abstract data type) , programming language , medicine , dentistry
In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.