Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T01:57:54.301Z Has data issue: false hasContentIssue false
  • English
  • Français

On the existence of large p-ideals

Published online by Cambridge University Press:  12 March 2014

Winfried Just ,
A. R. D. Mathias ,
Karel Prikry  and
Petr Simon
Winfried Just
Affiliation:
University of Warsaw, Warsaw, Poland Department of Mathematics, Charles University, 186 00 Prague 8, Czechoslovakia
A. R. D. Mathias
Affiliation:
Erindale College, University of Toronto, Toronto, Canada Department of Mathematics, Charles University, 186 00 Prague 8, Czechoslovakia
Karel Prikry
Affiliation:
Peterhouse, Cambridge CB2 1RD, England Department of Mathematics, Charles University, 186 00 Prague 8, Czechoslovakia
Petr Simon
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 Department of Mathematics, Charles University, 186 00 Prague 8, Czechoslovakia
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the existence of p-ideals that are nonmeagre subsets of (ω) under various set-theoretic assumptions.

Keywords

Idealp-pointcovering lemmascaleBanach space.
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 457 - 465
Copyright
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[B]Burzyk, J., An example of a noncomplete normed N-space, Bulletin of the Polish Academy of Sciences. Mathematics, vol. 35 (1987), pp. 449–455.Google Scholar
[BD]Baumgartner, J. E. and Dordal, P., Adjoining dominating functions, this Journal, vol. 50 (1985), pp. 94–101.Google Scholar
[DJ]Dodd, A. J. and Jensen, R. B., The covering lemma for L[U], Annals of Mathematical Logic, vol. 22 (1982), pp. 127–135.CrossRefGoogle Scholar
[FZ]Frankiewicz, R. and Zbierski, P., Strongly discrete subsets of ω*, Fundamenta Mathematicae, vol. 129(1988), pp. 173–180.CrossRefGoogle Scholar
[J]Just, W., A class of ideals over ω generalizing p-poinls, preprint, University of Warsaw, Warsaw, 1986.Google Scholar
[Je]Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[K]Ketonen, J., On the existence of P-points in the Stone-Čech compactification of integers, Fundamenta Mathematicae, vol. 92 (1976), pp. 91–94.CrossRefGoogle Scholar
[K1]Klis, Cz., An example of noncomplete normed k-space, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 26 (1978), pp. 415–420.Google Scholar
[M1]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-Verlag, Berlin, 1977, pp. 375–384.CrossRefGoogle Scholar
[M2]Mathias, A. R. D., A remark on rare filters, Infinite and finite sets, Colloquia Mathematica Societatis János Bolyai, vol. 10, North-Holland, Amsterdam, 1975, Part III, pp. 1095–1097.Google Scholar
[M3]Mathias, A. R. D., On a generalization of Ramsey's theorem, Fellowship dissertation, Peterhouse, Cambridge, 1969.Google Scholar
[M4]Mathias, A. R. D., Happy families, Annals of Mathematical Logic, vol. 11 (1977), pp. 59–111.CrossRefGoogle Scholar
[P]Prikry, K., On a theorem of Mathias, handwritten notes, 1978.Google Scholar
[R]Rothberger, F., On some problems of Hausdorff and Sierpiński, Fundamenta Mathematicae, vol. 35 (1948), pp. 29–46.CrossRefGoogle Scholar
[Ru]Rudin, W., Homogeneity problems in the theory of Čech compactifications, Duke Mathematical Journal, vol. 23 (1956), pp. 409–419.Google Scholar
[S]Sierpiński, W., Hypothèse de continu, Monografje Matematyczne, vol. 4, Z. Subwencji Funduszu Kultury Narodowej, Warsaw and Łwow, 1934.Google Scholar
[Sh]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[Sm]Simon, P., Private communication, 01, 1986.Google Scholar
[T]Talagrand, M., Compacts de fonctions mesurables et filtres non mesurables, Studia Mathematica, vol. 67 (1980), pp. 113–143.CrossRefGoogle Scholar
[vD]van Douwen, E. K., The integers and topology, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 111–167.CrossRefGoogle Scholar
[W]Wimmers, E., The Shelah P-point independence theorem, Israel Journal of Mathematics, vol. 43 (1982), pp. 28–48.CrossRefGoogle Scholar