Rapid ultrafilters and summable ideals
FLAŠKOVÁ, J. Rapid ultrafilters and summable ideals. Varšava, Polsko, 2012.
|Anglický název:||Rapid ultrafilters and summable ideals|
|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.|