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 ω₂ and of height ω · ω such that for all α < ω₁· ω · ω, E has a winning strategy in the Ehrenfeucht-Fraïssé game of length α. The main tool is the notion of a club-guessing sequence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-3-2,
author = {Tapani Hyttinen},
title = {Club-guessing and non-structure of trees},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {237-249},
zbl = {0974.03042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-3-2}
}
Tapani Hyttinen. Club-guessing and non-structure of trees. Fundamenta Mathematicae, Tome 167 (2001) pp. 237-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm168-3-2/