Cardinal coefficients associated to certain orders on ideals
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We study cardinal invariants connected to certain classical orderings on the family of ideals on ω. We give topological and analytic characterizations of these invariants using the idealized version of Fréchet-Urysohn property and, in a special case, using sequential properties of the space of finitely-supported probability measures with the weak* topology. We investigate consistency of some inequalities between these invariants and classical ones, and other related combinatorial questions. At last, we discuss maximality properties of almost disjoint families related to certain ordering on ideals.
KeywordsKatětov-order Analytic ideals Cardinal invariants of the continuum Almost disjoint families Frechet-Urysohn property Weak* topology
Mathematics Subject Classification (2000)03E17 03E35 03E75
A part of the paper was born in a fertile atmosphere of the Winter school on Abstract Analysis (Section Topology) 2010 in Hejnice, Czech Republic. The authors want to thank the occupants of the smokers room in Hejnice, particularly Prof. Petr Simon and Prof. Bohuslav Balcar, for interesting discussions about the subject of this paper. We would also like to thank Prof. Andreas Blass for his valuable remarks on the Katětov-order.
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