Long Strong Chains of Subsets of ${\omega }_1$

Abstract

We force the existence of a chain of length ${\omega }_3$ in $[{\omega }_1{]}^{{\omega }_1}$ 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.

31 pages