On some ideal related to the ideal (v 0 )

Piotr Kalemba

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

top
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).

How to cite

top

Piotr Kalemba. " On some ideal related to the ideal (v 0 ) ." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/270958>.

@article{PiotrKalemba2015,
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).},
author = {Piotr Kalemba},
journal = {Open Mathematics},
keywords = {Ideal (v0); Ideal isomorphism; Ideal type; Continuum hypothesis},
language = {eng},
number = {1},
pages = {null},
title = { On some ideal related to the ideal (v 0 ) },
url = {http://eudml.org/doc/270958},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Piotr Kalemba
TI - On some ideal related to the ideal (v 0 )
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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).
LA - eng
KW - Ideal (v0); Ideal isomorphism; Ideal type; Continuum hypothesis
UR - http://eudml.org/doc/270958
ER -

References

top
  1. [1] Balcar B., Hernández-Hernández F., Hrušák M., Combinatorics of dense subsets of the rationals, Fund. Math., 2004, 183, 59–80 Zbl1051.03038
  2. [2] Balcar B., Pelant J., Simon P., The space of ultrafilters on N covered by nowhere dense sets, Fund. Math., 1980, 110, 11–24 Zbl0568.54004
  3. [3] Brendle J., Strolling through paradise, Fund. Math., 1995, 148, 1–25 Zbl0835.03010
  4. [4] Halbeisen L., Making doughnuts of Cohen reals, Math. Log. Quart., 2003, 49, 173–178 Zbl1016.03054
  5. [5] Kalemba P., Plewik Sz., Wojciechowska A., On the ideal (v0), Cent. Eur. J. Math., 2008, 6, 218–227 [WoS] Zbl1151.03027
  6. [6] Plewik Sz., Ideals of nowhere Ramsey sets are isomorphic, J. Symbolic Logic,1994 , 59, 662–667 Zbl0809.04007
  7. [7] Repický M., Collapsing of cardinals in generalized Cohen’s forcing, Acta Universitatis Carolinae, Mathematica et Physica 1988, 29, 67–74 Zbl0673.03041

NotesEmbed ?

top

You must be logged in to post comments.