Lindelöf indestructibility, topological games and selection principles

Fundamenta Mathematicae

Volumn 210, Issue 1, 2010, Pages 1-46

  Scheepers, Marion ^a   Tall, Franklin D ^b  

^a BOISE STATE UNIVERSITY   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Cohen reals; Gerlits Nagy space; Hurewicz property; Indestructibly lindel f; Infinite game; Measurable cardinal; Menger property; Random reals; Real valued measurable cardinal; Rothberger space; Weakly compact cardinal

Indexed keywords

EID: 80955127338     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm210-1-1     Document Type: Article

References (60)

1. A. V. Arhangel'skii, On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955.
2. L. F. Aurichi and F. D. Tall, Lindelöf spaces which are indestructible, productive or D, Topology Appl., to appear.
3. T. Banakh and L. Zdomskyy, Separation properties between the σ-compactness and Hurewicz property, Topology Appl. 156 (2008), 10-15.
4. T. Bartoszyński and H. Judah, Borel images of sets of reals, Real Anal. Exchange 20 (1995), 1-23.
5. J. E. Baumgartner and F. D. Tall, Reflecting Lindelöfness, Topology Appl. 122 (2002), 35-49.
6. J. E. Baumgartner and E. van Douwen, Strong real-compactness and weakly measurable cardinals, ibid. 35 (1990), 239-251.
7. M. Bonanzinga, F. Cammaroto and M. Matveev, Projective versions of selection principles, ibid. 157 (2010), 874-893.
8. E. Borel, Sur la classification des ensembles de mesure nulle, Bull. Soc. Math. France 47 (1919), 97-125.
9. T. Carlson, Extending Lebesgue measure by infinitely many sets, Pacific J. Math. 115 (1984), 33-45.
10. -, Strong measure zero and strongly meager sets, Proc. Amer. Math. Soc. 118 (1993), 577-586.
11. J. Chaber and R. Pol, A remark on Fremlin-Miller theorem concerning the Menger property and Michael concentrated sets, manuscript, 2002.
12. P. Daniels and G. Gruenhage, The point-open type of subsets of the reals, Topology Appl. 37 (1990), 53-64.
13. A. Dow, Two applications of reflection and forcing to topology, in: Z. Frolík (ed.), General Topology and Its Relations to Modern Analysis and Algebra VI, Proc. Sixth Prague Topology Symposium 1986, Helderman, Berlin, 1988, 155-172.
14. A. Dow, F. D. Tall and W. A. R. Weiss, New proofs of the consistency of the normal Moore space conjecture, Topology Appl. 37 (1990), 33-51.
15. -, New proofs of the consistency of the normal Moore space conjecture II, ibid. 37 (1990), 115-129.
16. D. H. Fremlin and A. W. Miller, On some properties of Hurewicz, Menger and Rothberger, Fund. Math. 129 (1988), 17-33.
17. F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. 26 (1978), 445-449.
18. J. Gerlits and Zs. Nagy, Some properties of C(X), I, Topology Appl. 14 (1982), 151-161.
19. δ, Proc. Amer. Math. Soc. 118 (1993), 603-607.
20. R. Grunberg, L. R. Junqueira and F. D. Tall, Forcing and normality, Topology Appl. 84 (1998), 45-174.
21. W. Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1925), 401-425.
22. -, Über Folgen stetiger Funktionen, Fund. Math. 9 (1927), 193-204.
23. A. Iwasa, Covering properties and Cohen forcing, Topology Proc. 31 (2007), 553-559.
24. T. Jech, Set Theory, 2nd ed., Springer, 1997.
25. H. Judah, S. Shelah and W. H. Woodin, The Borel Conjecture, Ann. Pure Appl. Logic 50 (1990), 255-269.
26. I. Juhász, Cardinal Functions in Topology-Ten Years Later, Math. Centrum, Amsterdam, 1980.
27. W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, Combinatorics of open covers (II), Topology Appl. 73 (1996), 241-266.
28. M. Kada, Preserving the Lindelöf property under forcing extensions, Topology Proc., to appear.
29. R. W. Knight, A topological application of flat morasses, Fund. Math. 194 (2007), 45-66.
30. Lj. D. R. Kočinac and M. Scheepers, Combinatorics of open covers (VII): Groupability, ibid. 179 (2003), 131-155. (Pubitemid 38516545)
31. 1, Proc. Amer. Math. Soc. 130 (2002), 2777-2787.
32. R. Laver, On the consistency of Borel's conjecture, Acta Math. 137 (1976), 151-169.
33. A. Lévy and R. M. Solovay, Measurable cardinals and the Continuum Hypothesis, Israel J. Math. 5 (1967), 234-248.
34. K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik, Wiener Akademie, Wien 133 (1924), 421-444.
35. J. T. Moore, A solution to the L-space problem, J. Amer. Math. Soc. 19 (2006), 717-736.
36. J. Nagata, On the countable sum of zero-dimensional spaces, Fund. Math. 48 (1960), 1-14.
37. A. Nowik, M. Scheepers and T. Weiss, The algebraic sum of sets of real numbers with strong measure zero, J. Symbolic Logic 63 (1998), 301-324.
38. J. Pawlikowski, Undetermined sets of point-open games, Fund. Math. 144 (1994), 279-285.
39. -, Strongly meager sets and subsets of the plane, ibid. 156 (1998), 279-287. (Pubitemid 128339436)
40. E. Pearl (ed.), Open Problems in Topology II, Elsevier, 2007.
41. F. Rothberger, Eine Verschärfung der Eigenschaft C, Fund. Math. 30 (1938), 50-55.
42. M. Scheepers, Combinatorics of open covers (I): Ramsey theory, Topology Appl. 69 (1996), 31-62. (Pubitemid 126665933)
43. -, Selection principles and Sierpiński sets, Acta Math. Sinica 23 (2007), 1153-1162.
44. M. Scheepers and B. Tsaban, The combinatorics of Borel covers, Topology Appl. 121 (2002), 357-382. (Pubitemid 36794891)
45. S. Shelah, On some problems in general topology, in: Contemp. Math. 192 (1996), 91-101.
46. S. Shelah and L. J. Stanley, S-Forcing I, A "black-box" theorem for morasses, with applications to super Souslin trees, Israel J. Math. 43 (1982), 185-224.
47. W. Sierpiński, Sur un ensemble non dénombrable, dont toute image continue est de mesure nulle, Fund. Math. 11 (1928), 301-304.
48. Y. M. Smirnov, On universal spaces for certain classes of infinite-dimensional spaces, Amer. Math. Soc. Transl. (2) 21 (1962), 35-50.
49. R. M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory, Proc. Sympos. Pure Math. 13, Amer. Math. Soc., 1971, 397-428.
50. J. Steprāns, Combinatorial consequences of adding Cohen reals, in: Israel Math. Conf. Proc. 6, Bar-Ilan Univ., 1993, 583-617.
51. δ, Topology Appl. 63 (1995), 21-38.
52. -, Lindelöf spaces which are Menger, Hurewicz, Alster, productive or D, ibid., to appear.
53. R. Telgársky, On games of Topsøe, Math. Scand. 54 (1984), 170-176.
54. S. Todorčević, Aronszajn orderings, Publ. Inst. Math. 57 (71) (1995), 29-46.
55. B. Tsaban, SPM Bulletin 18 (2006), p. 7 (http://arxiv.org/PScache/math/ pdf/0609/0609401v1.pdf).
56. -, Selection principles and special sets of reals, in [40], 91-108.
57. B. Tsaban and L. Zdomskyy, Combinatorial images of sets of reals and semifilter trichotomy, J. Symbolic Logic 73 (2008), 1278-1288.
58. -, Scales, fields and a problem of Hurewicz, J. Eur. Math. Soc. 10 (2008), 837-866.
59. D. Velleman, Morasses, diamond and forcing, Ann. Math. Logic 23 (1982), 199-281.
60. L. Zdomskyy, A semifilter approach to selection principles, Comment. Math. Univ. Carolin. 46 (2005), 525-539.