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Displaying similar documents to “Strong sequences and partition relations”

A note on strong negative partition relations

Todd Eisworth (2009)

Fundamenta Mathematicae

Similarity:

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...

Ramseyan ultrafilters

Lorenz Halbeisen (2001)

Fundamenta Mathematicae

Similarity:

We investigate families of partitions of ω which are related to special coideals, so-called happy families, and give a dual form of Ramsey ultrafilters in terms of partitions. The combinatorial properties of these partition-ultrafilters, which we call Ramseyan ultrafilters, are similar to those of Ramsey ultrafilters. For example it will be shown that dual Mathias forcing restricted to a Ramseyan ultrafilter has the same features as Mathias forcing restricted to a Ramsey ultrafilter....