A note on strong negative partition relations

• Autorzy: Todd Eisworth
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E02: Partition relations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 202
• Numer: 2
• Strony: 97-123

Daty

wydano

2009

Twórcy

autor

Todd Eisworth

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

Identyfikatory

DOI

10.4064/fm202-2-1