Geodesic
Club-guessing and non-structure of trees
Tapani Hyttinen1
1 Department of Mathematics P.O. Box 4 00014 University of Helsinki Finland
Fundamenta Mathematicae, Tome 168 (2001) no. 3, pp. 237-249

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm168-3-2
Keywords: study possibilities constructing zfc without additional assumptions strongly equivalent non isomorphic trees regular power example there non isomorphic trees power omega height omega cdot omega alpha omega cdot omega cdot omega has winning strategy ehrenfeucht fra accent game length alpha main tool notion club guessing sequence

Tapani Hyttinen 1

1 Department of Mathematics P.O. Box 4 00014 University of Helsinki Finland 
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Tapani Hyttinen. Club-guessing and non-structure of trees. Fundamenta Mathematicae, Tome 168 (2001) no. 3, pp. 237-249. doi: 10.4064/fm168-3-2

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