Geodesic
A note on strong negative partition relations
Todd Eisworth1
1 Department of Mathematics Ohio University Athens, OH 45701, U.S.A.
Fundamenta Mathematicae, Tome 202 (2009) no. 2, pp. 97-123

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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.
DOI : 10.4064/fm202-2-1
Keywords: analyze natural function definable scale singular cardinal obtain strong negative square brackets partition relations successors singular cardinals proof main result makes club guessing corollary obtain fairly easy proof difficult result shelah connecting weak saturation certain club guessing ideal strong failures square brackets partition relations investigate strength weak saturation ideals obtain results stationary reflection

Todd Eisworth 1

1 Department of Mathematics Ohio University Athens, OH 45701, U.S.A. 
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Todd Eisworth. A note on strong negative partition relations. Fundamenta Mathematicae, Tome 202 (2009) no. 2, pp. 97-123. doi: 10.4064/fm202-2-1

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