A game-theoretic proof of Shelah's theorem on labeled trees
Logic
2019-08-08 v1
Abstract
We give a new proof of a theorem of Shelah which states that for every family of labeled trees, if the cardinality of the family is much larger (in the sense of large cardinals) than the cardinality of the set of labels, more precisely if the partition relation holds, then there is a homomorphism from one labeled tree in the family to another. Our proof uses a characterization of such homomorphisms in terms of games.
Cite
@article{arxiv.1908.02442,
title = {A game-theoretic proof of Shelah's theorem on labeled trees},
author = {Trevor M. Wilson},
journal= {arXiv preprint arXiv:1908.02442},
year = {2019}
}