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Summer 1995 Partition Principles and Infinite Sums of Cardinal Numbers
Masasi Higasikawa
Notre Dame J. Formal Logic 36(3): 425-434 (Summer 1995). DOI: 10.1305/ndjfl/1040149358

Abstract

The Axiom of Choice implies the Partition Principle and the existence, uniqueness, and monotonicity of (possibly infinite) sums of cardinal numbers. We establish several deductive relations among those principles and their variants: the monotonicity follows from the existence plus uniqueness; the uniqueness implies the Partition Principle; the Weak Partition Principle is strictly stronger than the Well-Ordered Choice.

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Masasi Higasikawa. "Partition Principles and Infinite Sums of Cardinal Numbers." Notre Dame J. Formal Logic 36 (3) 425 - 434, Summer 1995. https://doi.org/10.1305/ndjfl/1040149358

Information

Published: Summer 1995
First available in Project Euclid: 17 December 2002

zbMATH: 0843.03027
MathSciNet: MR1351415
Digital Object Identifier: 10.1305/ndjfl/1040149358

Subjects:
Primary: 03E25
Secondary: 03E10 , 03E35

Rights: Copyright © 1995 University of Notre Dame

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Vol.36 • No. 3 • Summer 1995
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