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Archive for Mathematical Logic

, Volume 51, Issue 1–2, pp 187–202 | Cite as

Cardinal coefficients associated to certain orders on ideals

  • Piotr Borodulin-NadziejaEmail author
  • Barnabás Farkas
Open Access
Article

Abstract

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.

Keywords

Katětov-order Analytic ideals Cardinal invariants of the continuum Almost disjoint families Frechet-Urysohn property Weak* topology 

Mathematics Subject Classification (2000)

03E17 03E35 03E75 

Notes

Acknowledgements

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.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland
  2. 2.Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary

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