The PCF Conjecture and Large Cardinals

Journal of Symbolic Logic 73 (2):674 - 688 (2008)
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
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    Thomas Jech (1995). Singular Cardinals and the Pcf Theory. Bulletin of Symbolic Logic 1 (4):408-424.
    Saharon Shelah (2000). Applications of PCF Theory. Journal of Symbolic Logic 65 (4):1624-1674.

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