Partition theorems from creatures and idempotent ultrafilters

Details Partition theorems from creatures and idempotent ultrafilters Partition theorems from creatures and idempotent ultrafilters

2010-05-17

arxiv.org/abs/1005.2803v2

Mathematics

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Scientific paper

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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