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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
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Abstract

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

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