Dow’s Principle and Q-Sets
Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 13-24

Voir la notice de l'article provenant de la source Cambridge University Press

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 $q$ .
DOI : 10.4153/CMB-1999-002-2
Mots-clés : 03E05, 03E35, 54A35, Q-set, cardinal invariants of the continuum, pseudointersection number, MA(σ-centered), Dow’s principle, almost disjoint family, almost disjointness principle, iterated forcing
Brendle, Jörg. Dow’s Principle and Q-Sets. Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 13-24. doi: 10.4153/CMB-1999-002-2
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[BJ] [BJ] Bartoszyński, T. and Judah, H., Set Theory, On the structure of the real line. A. K. Peters, Wellesley, 1995. Google Scholar

[BD] [BD] Baumgartner, J. and Dordal, P., Adjoining dominating functions. J. Symbolic Logic 50 (1985), 94–101. Google Scholar

[Be] [Be] Bell, M. G., On the combinatorial principle P(c). Fund. Math. 114 (1981), 149–157. Google Scholar

[BJS] [BJS] Brendle, J., Judah, H. and Shelah, S., Combinatorial properties of Hechler forcing. Ann. Pure Appl. Logic 58 (1992), 185–199. Google Scholar

[Do] [Do] Dow, A., On compact separable radial spaces. Preprint, 1996. Google Scholar

[He] [He] Heath, R. W., Screenability, pointwise paracompactness and metrization of Moore spaces. Canad. J. Math. 16 (1964), 763–770. Google Scholar

[Je] [Je] Jech, T., Set theory. Academic Press, San Diego, 1978. Google Scholar

[Ku] [Ku] Kunen, K., Set theory. North-Holland, Amsterdam, 1980. Google Scholar

[Mi 1] [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] [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] [Mi 3] Miller, A., Descriptive Set Theory and Forcing. Springer Lecture Notes in Logic 4, Berlin, Heidelberg, New York, 1995. Google Scholar

[Ta] [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] [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] [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

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