Asperó, David and Mota, Miguel Angel
(2017)
*Measuring club-sequences together with the continuum large.*
Journal of Symbolic Logic, 82 (3).
pp. 1066-1079.
ISSN 0022-4812

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## Abstract

Measuring says that for every sequence $(C_\delta)_{\delta<\omega_1}$ with each $C_\delta$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta\in C$,a tail of $C\cap\delta$ 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 models as side conditions and with symmetry constraints imposed on its initial segments. One interesting feature of this iteration is that it adds dominating functions $f:\omega_1\longrightarrow\omega_1$ mod. countable at each of its stages.

Item Type: | Article |
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Uncontrolled Keywords: | measuring,large continuum,iterated forcing with symmetric systems of models as side conditions |

Faculty \ School: | Faculty of Science > School of Mathematics |

UEA Research Groups: | Faculty of Science > Research Groups > Logic |

Depositing User: | Pure Connector |

Date Deposited: | 13 Jan 2017 00:05 |

Last Modified: | 22 Oct 2022 02:05 |

URI: | https://ueaeprints.uea.ac.uk/id/eprint/62026 |

DOI: | 10.1017/jsl.2017.4 |

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