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ASPERÓ–MOTA ITERATION AND THE SIZE OF THE CONTINUUM
Part of
- Set theory
TERUYUKI YORIOKA
Journal:

The Journal of Symbolic Logic / Volume 88 / Issue 4 / December 2023

Published online by Cambridge University Press:

02 May 2022, pp. 1387-1420

Print publication:

December 2023
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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.