2010/05/31 by Andrzej Rosłanowski, Andrzej Roslanowski, Saharon Shelah
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics #Creatures #Geography #Graph Labeling and Dimension Problems #Idempotence #Mathematics #Natural (archaeology) #Partition (number theory) #math.CO #math.LO
paper · pdf · doi:10.1007/s00026-013-0184-7
published as Annals of Combinatorics: Volume 17, Issue 2 (2013), Page 353-378
arxiv created 2011/03/23 · openalex publication_date 2013/01/09 · arxiv updated 2015/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.