The tree property at all regular even cardinals

Abstract

Assuming the existence of a strong cardinal and a measurable cardinal above it, we construct a model of $ZFC$ in which for every singular cardinal $\delta$, $\delta$ is strong limit, $2^{\delta }={\delta }^{+3}$ and the tree property at ${\delta }^{++}$ holds. This answers a question of Friedman, Honzik and Stejskalova [8]. We also produce, relative to the existence of a strong cardinal and two measurable cardinals above it, a model of $ZFC$ in which the tree property holds at all regular even cardinals. The result answers questions of Friedman-Halilovic [5] and Friedman-Honzik [6].

arXiv commentComments are welcome

References in corpus (1)

• On a Question of Hamkins and Löwe on the modal logic of collapse forcing