Constructions in Ramsey theory: CONSTRUCTIONS IN RAMSEY THEORY
- Award ID(s):
- 1800746
- PAR ID:
- 10051471
- 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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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.more » « less
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