Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Cofinal families of compact subsets of an analytic set


Author: Howard Becker
Journal: Proc. Amer. Math. Soc. 106 (1989), 853-856
MSC: Primary 03E35; Secondary 54A35
DOI: https://doi.org/10.1090/S0002-9939-1989-0976359-9
MathSciNet review: 976359
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a question of van Douwen regarding the minimum cardinality of cofinal families of compact sets in certain topological spaces. We show that the question cannot be answered in ZFC.


References [Enhancements On Off] (What's this?)

  • [1] E. K. van Douwen, Problem 11 , Topology Proc. 6 (1981), 443.
  • [2] -, The integers and topology, in Handbook of Set Theoretic Topology, (K. Kunen and J. E. Vaughan, eds.) North-Holland, Amsterdam, 1984, 111-167. MR 776619 (85k:54001)
  • [3] F. van Engelen, Cofinal families of compacta in separable metric spaces, Proc. Amer. Math. Soc. 104 (1988), 1271-1273. MR 969060 (90g:54031)
  • [4] D. H. Fremlin, Consequences of Martin's axiom, Cambridge Univ. Press, Cambridge, 1984.
  • [5] S. H. Hechler, On the existence of certain cofinal subsets of $ {\omega ^\omega }$ , in Axiomatic Set Theory, (T. J. Jech, ed.), Proc. Symp. Pure Math., vol. 13, Part 2, Amer. Math. Soc, Providence, R.I., 1974, pp. 155-173. MR 0360266 (50:12716)
  • [6] T. J. Jech, Set theory, Academic Press, 1978.
  • [7] A. S. Kechris, A. Louveau, and W. H. Woodin, The structure of $ \sigma $-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263-288. MR 879573 (88f:03042)
  • [8] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Annals Math. Logic 2 (1970), 143-178. MR 0270904 (42:5787)
  • [9] Y. N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1980. MR 561709 (82e:03002)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E35, 54A35

Retrieve articles in all journals with MSC: 03E35, 54A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0976359-9
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society