Club-guessing and non-structure of trees

Tom 168 / 2001

Tapani Hyttinen Fundamenta Mathematicae 168 (2001), 237-249 MSC: Primary 03C75; Secondary 03E05. DOI: 10.4064/fm168-3-2


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.


  • Tapani HyttinenDepartment of Mathematics
    P.O. Box 4
    00014 University of Helsinki

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