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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 6, 2015

On some ideal related to the ideal (v0)

  • Piotr Kalemba
From the journal Open Mathematics

Abstract

The ideal (v0) is known in the literature and is naturally linked to the structure [ω]ω. We consider some natural counterpart of the ideal (v0) related in an analogous way to the structure Dense(ℚ) and investigate its combinatorial properties. By the use of the notion of ideal type we prove that under CH this ideal is isomorphic to (v0).

References

[1] Balcar B., Hernández-Hernández F., Hrušák M., Combinatorics of dense subsets of the rationals, Fund. Math., 2004, 183, 59–80 10.4064/fm183-1-4Search in Google Scholar

[2] Balcar B., Pelant J., Simon P., The space of ultrafilters on N covered by nowhere dense sets, Fund. Math., 1980, 110, 11–24 10.4064/fm-110-1-11-24Search in Google Scholar

[3] Brendle J., Strolling through paradise, Fund. Math., 1995, 148, 1–25 10.4064/fm-148-1-1-25Search in Google Scholar

[4] Halbeisen L., Making doughnuts of Cohen reals, Math. Log. Quart., 2003, 49, 173–178 10.1002/malq.200310016Search in Google Scholar

[5] Kalemba P., Plewik Sz., Wojciechowska A., On the ideal (v0), Cent. Eur. J. Math., 2008, 6, 218–227 10.2478/s11533-008-0021-0Search in Google Scholar

[6] Plewik Sz., Ideals of nowhere Ramsey sets are isomorphic, J. Symbolic Logic,1994 , 59, 662–667 10.2307/2275415Search in Google Scholar

[7] Repický M., Collapsing of cardinals in generalized Cohen’s forcing, Acta Universitatis Carolinae, Mathematica et Physica 1988, 29, 67–74 Search in Google Scholar

Received: 2014-9-12
Accepted: 2014-4-3
Published Online: 2015-7-6

©2015 Piotr Kalemba

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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