PP-2009-21: Cofinality and Measurability of the First Three Uncountable Cardinals

PP-2009-21: Apter, Arthur W. and Jackson, Stephen C. and Löwe, Benedikt (2009) Cofinality and Measurability of the First Three Uncountable Cardinals. [Report]

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This paper discusses models of set theory without the Axiom of Choice. We investigate all possible patterns of the cofinality function and the distribution of measurability on the first three uncountable cardinals. The result relies heavily on a strengthening of an unpublished result of Kechris: we prove (under AD) that there is a cardinal κ such that the triple (κ, κ+ , κ++) satisfies the strong polarized partition property.

Item Type: Report
Report Nr: PP-2009-21
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: Axiom of Choice, Cardinals, Partition Properties
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/351

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