A note on strong negative partition relations

Volume 202 / 2009

Todd Eisworth Fundamenta Mathematicae 202 (2009), 97-123 MSC: Primary 03E02. DOI: 10.4064/fm202-2-1


We analyze a natural function definable from a scale at a singular cardinal, and use it to obtain some strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main result makes use of club-guessing, and as a corollary we obtain a fairly easy proof of a difficult result of Shelah connecting weak saturation of a certain club-guessing ideal with strong failures of square-brackets partition relations. We then investigate the strength of weak saturation of such ideals and obtain some results on stationary reflection.


  • Todd EisworthDepartment of Mathematics
    Ohio University
    Athens, OH 45701, U.S.A.

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