Notre Dame Journal of Formal Logic

Partition Principles and Infinite Sums of Cardinal Numbers

Masasi Higasikawa


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

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

First available in Project Euclid: 17 December 2002

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Zentralblatt MATH identifier

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


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.

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