TY - JOUR
T1 - Partition Theorems from Creatures and Idempotent Ultrafilters
AU - Rosłanowski, Andrzej
AU - Shelah, Saharon
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - norms on possibilities
KW - partition theorems
KW - ultrafilters
UR - http://www.scopus.com/inward/record.url?scp=84878208167&partnerID=8YFLogxK
U2 - 10.1007/s00026-013-0184-7
DO - 10.1007/s00026-013-0184-7
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AN - SCOPUS:84878208167
SN - 0218-0006
VL - 17
SP - 353
EP - 378
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 2
ER -