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Q-pointness, P-pointness and feebleness of ideals

Published online by Cambridge University Press:  12 March 2014

Pierre Matet  and
Janusz Pawlikowski
Pierre Matet
Affiliation:
Mathematiques, Universite de Caen, Campus II, B.P. 5186, 14032 Caen Cedex, France, E-mail: matet@math.unicaen.fr
Janusz Pawlikowski
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, PL. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: pawlikow@math.uni.wroc.pl
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Abstract

We study the degree of (weak) (Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 235 - 261
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1]Balcar, B. and Simon, P., Disjoint refinement, Handbook of Boolean algebras (Monk, J. D. and Bonnet, R., editors), vol. 2, North-Holland, 1989, pp. 333–388.Google Scholar
[2]Baumgartner, J. E., Taylor, A. D., and Wagon, S., Structural properties of ideals, Dissertationes Mathematicae, vol. 197 (1982).Google Scholar
[3]Blass, A., Groupwise density and related cardinals, Archive for Mathematical Logic, vol. 30 (1990), pp. 1–11.CrossRefGoogle Scholar
[4]Blass, A. and Shelah, S., There may be simple , and -points and the Rudin-Keisler ordering may be downward directed, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 213–243.CrossRefGoogle Scholar
[5]Canjar, R. M., On the generic existence of special ultrafilters, Proceedings of the American Mathematical Society, vol. 110 (1990), pp. 233–241.CrossRefGoogle Scholar
[6]Dordal, P. L., Towers in [ω]ω and ωω, Annals of Pure and Applied Logic, vol. 45 (1989), pp. 247–276.CrossRefGoogle Scholar
[7]Frankiewicz, R. and Zbierski, P., Strongly discrete subsets of ω*, Fundamenta Mathematicae, vol. 129 (1988), pp. 173–180.CrossRefGoogle Scholar
[8]Hechler, S.H., On the existence of certain cofinal subsets of ωω, Axiomatic set theory (Proceedings of Symposia in Pure Mathematics, volume 13, part II) (Jech, T., editor), American Mathematical Society, 1974, pp. 155–173.Google Scholar
[9]Jech, T. J., Set theory, Academic Press, 1978.Google Scholar
[10]Just, W., Mathias, A. R. D., Prikry, K., and Simon, P., On the existence of large p-ideals, this Journal, vol. 55 (1990), pp. 457–465.Google Scholar
[11]Laflamme, C., Strong meager properties for filters, Fundamenta Mathematicae, vol. 146 (1995), pp. 283–293.CrossRefGoogle Scholar
[12]Landver, A., Singular Baire numbers and related topics, Ph.D. thesis, University of Wisconsin, Madison, Wisconsin, 1990.Google Scholar
[13]Louveau, A., Une méthode topologique pour l'étude de la propriété de Ramsey, Israel Journal of Mathematics, vol. 23 (1976), pp. 97–116.CrossRefGoogle Scholar
[14]Matet, P., Combinatorics and forcing with distributive ideals, Annals of Pure and Applied Logic, vol. 86 (1997), pp. 137–201.CrossRefGoogle Scholar
[15]Matet, P. and Pawlikowski, J., Ideals over ω and cardinal invariants of the continuum, this Journal, vol. 63 (1998), pp. 1040–1054.Google Scholar
[16]Matet, P., Rosłanowski, A., and Shelah, S., Cofinality of the nonstationary ideal, preprint.Google Scholar
[17]Mathias, A. R. D., A remark on rare filters, Infinite and finite sets (Colloquia Mathematica Societatis János Bolyai, volume 10, part III) (Hajnal, A., Rado, R., and Sós, V. T., editors), North-Holland, 1975, pp. 1095–1097.Google Scholar
[18]Mathias, A. R. D., 0# and the p-point problem, Higher set theory (Müller, G. and Scott, D., editors), Lecture Notes in Mathematics, vol. 669, Springer, 1978, pp. 375–384.CrossRefGoogle Scholar
[19]Miller, A. W., There are no Q-points in Layer's model for the Borel conjecture, Proceedings of the American Mathematical Society, vol. 78 (1980), pp. 103–106.Google Scholar
[20]Pawlikowski, J., Powers of transitive bases of measure and category, Proceedings of the American Mathematical Society, vol. 93 (1985), pp. 719–729.CrossRefGoogle Scholar
[21]Shelah, S., Vive la différence I: non isomorphism of ultrapowers of countable models, Set theory of the continuum (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, 1992, pp. 357–405.CrossRefGoogle Scholar
[22]Talagrand, M., Compacts de fonctions mesurables etfiltres non mesurables, Studia Mathematica, vol. 67 (1980), pp. 13–43.CrossRefGoogle Scholar
[23]Tall, F. D., Some applications of a generalized Martin's axiom, Topology and its Applications, vol. 57 (1994), pp. 215–248.CrossRefGoogle Scholar
[24]van Douwen, E. K., The integers and topology, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, 1984, pp. 113–167.Google Scholar