Journal of Symbolic Logic

The PCF conjecture and large cardinals

Luís Pereira

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Abstract

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

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

Dates
First available: 16 April 2008

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1208359066

Digital Object Identifier
doi:10.2178/jsl/1208359066

Zentralblatt MATH identifier
1153.03024

Mathematical Reviews number (MathSciNet)
MR2414471

Subjects
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

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

Citation

Pereira, Luís. The PCF conjecture and large cardinals. Journal of Symbolic Logic 73 (2008), no. 2, 674--688. doi:10.2178/jsl/1208359066. http://projecteuclid.org/euclid.jsl/1208359066.


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