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RETRACTED – MEASURING CLUB-SEQUENCES TOGETHER WITH THE CONTINUUM LARGE

Part of: Set theory

Published online by Cambridge University Press:  08 September 2017

DAVID ASPERÓ  and
MIGUEL ANGEL MOTA
DAVID ASPERÓ
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA NORWICH NR4 7TJ, UKE-mail: [email protected]
MIGUEL ANGEL MOTA
Affiliation:
DEPARTAMENTO DE MATEMÁTICAS ITAM, MEXICO CITY 01080 MEXICOE-mail: [email protected]
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Abstract

Measuring says that for every sequence ${\left( {{C_\delta }} \right)_{\delta < {\omega _1}}}$ with each ${C_\delta }$ being a closed subset of δ there is a club $C \subseteq {\omega _1}$ such that for every $\delta \in C$ , a tail of $C\mathop \cap \nolimits \delta$ is either contained in or disjoint from ${C_\delta }$ . We answer a question of Justin Moore by building a forcing extension satisfying measuring together with ${2^{{\aleph _0}}} > {\aleph _2}$ . The construction works over any model of ZFC + CH and can be described as a finite support forcing iteration with systems of countable structures as side conditions and with symmetry constraints imposed on its initial segments. One interesting feature of this iteration is that it adds dominating functions $f:{\omega _1} \to {\omega _1}$ mod. countable at each stage.

Keywords

measuringlarge continuumiterated forcing with symmetric systems of models as side conditions

MSC classification

Primary: 03E50: Continuum hypothesis and Martin's axiom
Secondary: 03E35: Consistency and independence results 03E05: Other combinatorial set theory 03E17: Cardinal characteristics of the continuum
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 1066 - 1079
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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