Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T17:56:34.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Dow’s Principle and Q-Sets

Published online by Cambridge University Press:  20 November 2018

Jörg Brendle
Jörg Brendle*
Affiliation:
Department of Mathematics Bradley Hall Dartmouth College Hanover, New Hampshire 03755 U.S.A.The Graduate School of Science and Technology Kobe University Rokko-dai 1-1, Nada, Kobe 657-8501 Japan, email: jobr@michelangelo.mathematik.uni-tuebingen.de email: brendle@pascal.seg.kobe-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A $Q$ -set is a set of reals every subset of which is a relative ${{G}_{\delta }}$ . We investigate the combinatorics of $Q$ -sets and discuss a question of Miller and Zhou on the size $q$ of the smallest set of reals which is not a $Q$ -set. We show in particular that various natural lower bounds for $q$ are consistently strictly smaller than $q$ .

Keywords

03E0503E3554A35Q-setcardinal invariants of the continuumpseudointersection numberMA(σ-centered)Dow’s principlealmost disjoint familyalmost disjointness principleiterated forcing

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 1 , 01 March 1999, pp. 13 - 24
Copyright
Copyright © Canadian Mathematical Society 1999

References

[BJ] Bartoszyński, T. and Judah, H., Set Theory, On the structure of the real line. A. K. Peters, Wellesley, 1995.Google Scholar
[BD] Baumgartner, J. and Dordal, P., Adjoining dominating functions. J. Symbolic Logic 50 (1985), 94–101.Google Scholar
[Be] Bell, M. G., On the combinatorial principle P(c). Fund. Math. 114 (1981), 149–157.Google Scholar
[BJS] Brendle, J., Judah, H. and Shelah, S., Combinatorial properties of Hechler forcing. Ann. Pure Appl. Logic 58 (1992), 185–199.Google Scholar
[Do] Dow, A., On compact separable radial spaces. Preprint, 1996.Google Scholar
[He] Heath, R. W., Screenability, pointwise paracompactness and metrization of Moore spaces. Canad. J. Math. 16 (1964), 763–770.Google Scholar
[Je] Jech, T., Set theory. Academic Press, San Diego, 1978.Google Scholar
[Ku] Kunen, K., Set theory. North-Holland, Amsterdam, 1980.Google Scholar
[Mi 1] Miller, A., Special subsets of the real line. Handbook of set-theoretic topology (Eds. K. Kunen and J. E. Vaughan), North-Holland, Amsterdam, 1984, 201–233.Google Scholar
[Mi 2] Miller, A., Arnie Miller's problem list. In: Set Theory of the Reals (Ed. H. Judah), Israel Mathematical Conference Proceedings 6, 1993, 645–654.Google Scholar
[Mi 3] Miller, A., Descriptive Set Theory and Forcing. Springer Lecture Notes in Logic 4, Berlin, Heidelberg, New York, 1995.Google Scholar
[Ta] Tall, F., Normality versus collectionwise normality. Handbook of set-theoretic topology (Eds. K. Kunen and J. E. Vaughan), North-Holland, Amsterdam, 1984, 685–732.Google Scholar
[vD] van Douwen, E. K., The integers and topology. Handbook of set-theoretic topology (Eds. K. Kunen and J. E. Vaughan), North-Holland, Amsterdam, 1984, 111–167.Google Scholar
[Va] Vaughan, J., Small uncountable cardinals and topology. Open problems in topology (Eds. J. van Mill and G. Reed), North-Holland, 1990, 195–218.Google Scholar