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Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis |
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| Authors: | Arthur L. Rubin Jean E. Rubin |
| Abstract: | 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. |
| Keywords: | Axiom of choice Generalized continuum hypothesis Partition principle Trichotomy of cardinals |