Ma and lattice partitions

Serra Alves, Carlos

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Martin's axiom and partitions

S. Todorcevic, B. Velickovic (1987)

Compositio Mathematica

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Dualization of van Douwen diagram

Jacek Cichoń, Barbara Majcher-Iwanow, Bogdan Węglorz (1992)

Acta Universitatis Carolinae. Mathematica et Physica

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Ramseyan ultrafilters

Lorenz Halbeisen (2001)

Fundamenta Mathematicae

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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....