Partition theorems from creatures and idempotent ultrafilters
Logic
2015-03-17 v2 Combinatorics
Abstract
We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of the Hindman Theorem, so we prove the existence of idempotent ultrafilters with respect to suitable operation. Then we deduce partition theorems related to creature forcings.
Cite
@article{arxiv.1005.2803,
title = {Partition theorems from creatures and idempotent ultrafilters},
author = {Andrzej Roslanowski and Saharon Shelah},
journal= {arXiv preprint arXiv:1005.2803},
year = {2015}
}