Relations Between Some Cardinals in the Absence of the Axiom of Choice

Lorenz Halbeısen, Saharon Shelah

Type: Article

Publication Date: 2001-06-01

Citations: 26

DOI: https://doi.org/10.2307/2687776

Abstract

Abstract If we assume the axiom of choice, then every two cardinal numbers are comparable. In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice.

Locations

Bulletin of Symbolic Logic - View
arXiv (Cornell University) - View - PDF

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+	Consequences of the Axiom of Choice	1998	Paul Howard Jean Rubin
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+	On a Problem of Formal Logic	1930	Frank Plumpton Ramsey
+ PDF Chat	Consequences of arithmetic for set theory	1994	Lorenz Halbeisen Saharon Shelah
+	Transfinite Zahlen	1967	Heinz Bachmann
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