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Rapid ultrafilters and summable ideals

Citace: FLAŠKOVÁ, J. Rapid ultrafilters and summable ideals. Varšava, Polsko, 2012.
Jazyk publikace: eng
Anglický název: Rapid ultrafilters and summable ideals
Rok vydání: 2012
Autoři: RNDr. Jana Flašková Ph.D.
Abstrakt EN: It is known that rapid ultrafilters can be characterized as those ultrafilters which have a nonempty intersection with each tall summable ideal I_g. An ultrafilter u is called an I_g-ultrafilter if for every function f:N -> N there exists a set U in u such that f[U] belongs to I_g. Obviously, if an ultrafilter u is an I_g-ultrafilter for all tall summable ideals then u is rapid. However, if only one summable ideal I_g is considered, the analogous proposition need not be true. We prove under the assumption of Martin's Axiom for sigma-centered posets that for every tall summable ideal I_g there exists I_g-ultrafilter which is not rapid.
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