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Title: Constructions in Ramsey theory: CONSTRUCTIONS IN RAMSEY THEORY
Award ID(s):
1800746
PAR ID:
10051471
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Oxford University Press (OUP)
Date Published:
Journal Name:
Journal of the London Mathematical Society
Volume:
97
Issue:
2
ISSN:
0024-6107
Page Range / eLocation ID:
247 to 257
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied by the existence of appropriate homomorphisms between the algebraic structures. We make a connection between the two themes above, which allows us to prove some general Ramsey theorems for sequences. We give a new proof of the Furstenberg–Katznelson Ramsey theorem; in fact, we obtain a version of this theorem that is stronger than the original one. We answer in the negative a question of Lupini on possible extensions of Gowers’ Ramsey theorem. 
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