Journal of Symbolic Logic

The PCF conjecture and large cardinals

Luís Pereira

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We prove that a combinatorial consequence of the negation of the PCF conjecture for intervals, involving free subsets relative to set mappings, is not implied by even the strongest known large cardinal axiom.

Article information

J. Symbolic Logic Volume 73, Issue 2 (2008), 674-688.

First available in Project Euclid: 16 April 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E04: Ordered sets and their cofinalities; pcf theory 03E05: Other combinatorial set theory 03E10: Ordinal and cardinal numbers 03E35: Consistency and independence results 03E55: Large cardinals

PCF theory PCF conjecture free subsets continuous tree-like scales large cardinals


Pereira, Luís. The PCF conjecture and large cardinals. J. Symbolic Logic 73 (2008), no. 2, 674--688. doi:10.2178/jsl/1208359066.

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