Notre Dame Journal of Formal Logic

Partition Principles and Infinite Sums of Cardinal Numbers

Masasi Higasikawa

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 3 (1995), 425-434.

Dates
First available in Project Euclid: 17 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040149358

Digital Object Identifier
doi:10.1305/ndjfl/1040149358

Mathematical Reviews number (MathSciNet)
MR1351415

Zentralblatt MATH identifier
0843.03027

Subjects
Primary: 03E25: Axiom of choice and related propositions
Secondary: 03E10: Ordinal and cardinal numbers 03E35: Consistency and independence results

Citation

Higasikawa, Masasi. Partition Principles and Infinite Sums of Cardinal Numbers. Notre Dame J. Formal Logic 36 (1995), no. 3, 425--434. doi:10.1305/ndjfl/1040149358. https://projecteuclid.org/euclid.ndjfl/1040149358


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