Club-guessing and non-structure of trees
Volume 168 / 2001
Fundamenta Mathematicae 168 (2001), 237-249
MSC: Primary 03C75; Secondary 03E05.
DOI: 10.4064/fm168-3-2
Abstract
We study the possibilities of constructing, in ZFC without any additional assumptions, strongly equivalent non-isomorphic trees of regular power. For example, we show that there are non-isomorphic trees of power $\omega _{2}$ and of height $\omega \cdot \omega $ such that for all $\alpha <\omega _{1}\cdot \omega \cdot \omega $, $E$ has a winning strategy in the Ehrenfeucht–Fra\accent"7F ıssé game of length $\alpha $. The main tool is the notion of a club-guessing sequence.
