Partition theorems from creatures and idempotent ultrafilters

by Roslanowski and Shelah. [RoSh:957]
Annals Combinatorics, 2013
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.

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