The baire category theorem and cardinals of countable cofinality

Journal of Symbolic Logic 47 (2):275-288 (1982)
  Copy   BIBTEX

Abstract

Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, other ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,662

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
19 (#583,324)

6 months
2 (#279,538)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Game Ideals.Pierre Matet - 2009 - Annals of Pure and Applied Logic 158 (1-2):23-39.
Properties of Ideals on the Generalized Cantor Spaces.Jan Kraszewski - 2001 - Journal of Symbolic Logic 66 (3):1303-1320.

Add more citations

References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Internal Cohen Extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Handbook of Set-Theoretic Topology.Kenneth Kunen & Jerry E. Vaughan - 1987 - Journal of Symbolic Logic 52 (4):1044-1046.

Add more references