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ASPERÓ–MOTA ITERATION AND THE SIZE OF THE CONTINUUM

Part of: Set theory

Published online by Cambridge University Press:  02 May 2022

TERUYUKI YORIOKA
TERUYUKI YORIOKA*
Affiliation:
DEPARTMENT OF MATHEMATICS SHIZUOKA UNIVERSITY OHYA 836, SHIZUOKA 422-8529, JAPAN
*
E-mail: yorioka@shizuoka.ac.jp
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Abstract

In this paper we build an Asperó–Mota iteration of length $\omega _2$ that adds a family of $\aleph _2$ many club subsets of $\omega _1$ which cannot be diagonalized while preserving $\aleph _2$. This result discloses a technical limitation of some types of Asperó–Mota iterations.

Keywords

Asperó–Mota iterationthe size of the continuumclub sets

MSC classification

Primary: 03E35: Consistency and independence results
Secondary: 03E50: Continuum hypothesis and Martin's axiom

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 4 , December 2023 , pp. 1387 - 1420
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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Footnotes

The author is supported by Grant-in-Aid for Scientific Research (C) 18K03393, Japan Society for the Promotion of Science.

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