A new and stronger central sets theorem

• Autorzy: Dibyendu De , Neil Hindman , Dona Strauss
• Języki publikacji: EN

Abstrakty

EN

Furstenberg's original Central Sets Theorem applied to central subsets of ℕ and finitely many specified sequences in ℤ. In this form it was already strong enough to derive some very strong combinatorial consequences, such as the fact that a central subset of ℕ contains solutions to all partition regular systems of homogeneous equations. Subsequently the Central Sets Theorem was extended to apply to arbitrary semigroups and countably many specified sequences. In this paper we derive a new version of the Central Sets Theorem for arbitrary semigroups S which applies to all sequences in S at once. We show that the new version is strictly stronger than the original version applied to the semigroup (ℝ,+). And we show that the noncommutative versions are strictly increasing in strength.

Kategorie tematyczne

• 05D10: Ramsey theory
• 22A15: Structure of topological semigroups
• 54H13: Topological fields, rings, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 199
• Numer: 2
• Strony: 155-175

Daty

wydano

2008

Twórcy

autor

Dibyendu De

• Department of Mathematics, Krishnagar Women's College, Krishnagar, Nadia-741101, West Bengal, India

autor

Neil Hindman

• Department of Mathematics, Howard University, Washington, DC 20059, U.S.A.

autor

Dona Strauss

• Department of Pure Mathematics, University of Leeds, Leeds LS2 9J2, UK

Identyfikatory

DOI

10.4064/fm199-2-5