Crowded and selective ultrafilters under the Covering Property Axiom

Journal of Applied Analysis

Volumn 9, Issue 1, 2003, Pages 19-55

  Ciesielski, K ^a   Pawlikowski, J ^b  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b UNIVERSITY OF WROC AW   (Poland)

Author keywords

Almost disjoint; Covering; Crowded; Independence; P point; Rational numbers; Reaping; Selective; Ultrafilter

Indexed keywords

EID: 0345709488     PISSN: 14256908     EISSN: 18696082     Source Type: Journal    
DOI: 10.1515/JAA.2003.19     Document Type: Article

References (27)

1. Bartoszyński, T., Judah, H., Set Theory. On the Structure of the Real Line, A K Peters Ltd, Wellesley, MA, 1995.
2. Baumgartner, J., Laver, R., Iterated perfect-set forcing, Ann. Math. Logic 17(1979), 271-288.
3. Blass, A., Combinatorial cardinal characteristics of the continuum, in the "Handbook of Set Theory" (eds. M. Foreman, M. Magidor, and A. Kanamori), to appear.
4. Brodskiǐ, M. L., On some properties of sets of positive measure, Uspekhi Mat. Nauk (N. S.) 4, no. 3(31) (1949), 136-138.
5. Bukovsky, L., Kholshchevnikova, N. N., Repicky, M., Thin sets of harmonic analysis and infinite combinatorics, Real Anal. Exchange 20(2) (1994-95), 454-509.
6. Ciesielski, K., Set Theory for the Working Mathematician, London Math. Soc. Stud. Texts 39, Cambridge Univ. Press, Cambridge, 1997.
7. *5, 2002.
8. *.
9. * available.)
10. Coplakova, C, Hart, K. P., Crowded rational ultrafilters, Topology Appl. 97(1999), 79-84.
11. van Douwen, E. K., The integers and topology, in "Handbook of Set-Theoretic Topology" (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, 111-167.
12. van Douwen, E. K., Better closed ultrafilters on ℚ, Topology Appl. 47(3) (1992), 173-177.
13. Eggleston, H. G., Two measure properties of Cartesian product sets, Quart. J. Math. Oxford Ser. (2) 5(1954), 108-115.
14. Farah, I., Semiselective coideals, Mathematika 45(1998), 79-103.
15. Grigorieff, S., Combinatorics on ideals and forcing, Ann. Math. Logic 3(4) (1971), 363-394.
16. 1, J. Symbolic Logic 54(1) (1989), 1-15.
17. Hrusak, M., private communication (e-mail to K. Ciesielski), March 2000.
18. Jech, T., Set Theory, Academic Press, New York, 1978.
19. Kanovei, V., Non-Glimm-Effros equivalence relations at second projective level, Fund. Math. 154(1997), 1-35. (Pubitemid 127339710)
20. Kechris, A. S., Classical Descriptive Set Theory, Springer-Verlag, Berlin 1995.
21. Kunen, K., Some points in βN, Math. Proc. Cambridge Philos. Soc. 80(3) (1976), 385-398.
22. Laver, R., Products of infinitely many perfect trees, J. London Math. Soc. (2) 29(1984), 385-396.
23. Miller, A. W., Mapping a set of reals onto the reals, J. Symbolic Logic 48(1983), 575-584.
24. Miller, A. W., Special subsets of the real line, in "Handbook of Set-Theoretic Topology" (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, 201-233.
25. Steprāns, J., Sums of Darboux and continuous functions, Fund. Math. 146(1995), 107-120.
26. Vaughan, J. E., Small uncountable cardinals and topology, in "Open Problems in Topology" (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, 195-216.
27. Zapletal, J., Cardinal Invariants and Descriptive Set Theory, Mem. Amer. Math. Soc., to appear.