Long Strong Chains of Subsets of $ω_1$

Published: April 17, 2026PDF arXiv

Abstract

We force the existence of a chain of length $ω_3$ in $[ω_1]^{ω_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veličković-Venturi.

Long Strong Chains of Subsets of $ω_1$

David Asperó, Curial Gallart

math.LO

Published: April 17, 2026PDF arXiv

Abstract

We force the existence of a chain of length $ω_3$ in $[ω_1]^{ω_1}$ increasing modulo finite. The construction involves symmetric systems of models of two types as side conditions, introduced by the second author. This improves previous results of Koszmider and Veličković-Venturi.