Asperó–mota Iteration and the Size of the Continuum

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.