Combinatorics of ideals --- selectivity versus density

A. Kwela; P. Zakrzewski

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 2, page 261-266
  • ISSN: 0010-2628

Abstract

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This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.

How to cite

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Kwela, A., and Zakrzewski, P.. "Combinatorics of ideals --- selectivity versus density." Commentationes Mathematicae Universitatis Carolinae 58.2 (2017): 261-266. <http://eudml.org/doc/288180>.

@article{Kwela2017,
abstract = {This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.},
author = {Kwela, A., Zakrzewski, P.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ideals on natural numbers; ultrafilter topology},
language = {eng},
number = {2},
pages = {261-266},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Combinatorics of ideals --- selectivity versus density},
url = {http://eudml.org/doc/288180},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Kwela, A.
AU - Zakrzewski, P.
TI - Combinatorics of ideals --- selectivity versus density
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 2
SP - 261
EP - 266
AB - This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.
LA - eng
KW - ideals on natural numbers; ultrafilter topology
UR - http://eudml.org/doc/288180
ER -

References

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  6. Mathias A.R.D., 10.1016/0003-4843(77)90006-7, Ann. Math. Logic 12 (1977), no. 1, 59–111. Zbl0369.02041MR0491197DOI10.1016/0003-4843(77)90006-7
  7. Thümmel E., Ramsey theorems and topological dynamics, PhD. Thesis, Charles University of Prague, 1996. 
  8. Todorčević S., 10.1007/BFb0096295, Lecture Notes in Mathematics, 1652, Springer, Berlin, 1997. Zbl0953.54001MR1442262DOI10.1007/BFb0096295
  9. Todorčević S., 10.1006/aama.1997.0572, Adv. in Appl. Math. 20 (1998), no. 2, 220–252. MR1601383DOI10.1006/aama.1997.0572
  10. Todorčević S., Introduction to Ramsey Spaces, Annals of Mathematics Studies, 174, Princeton University Press, Princeton, 2010. MR2603812

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