A new and stronger central sets theorem

Dibyendu De, Neil Hindman, and Dona Strauss. "A new and stronger central sets theorem." Fundamenta Mathematicae 199.2 (2008): 155-175. <http://eudml.org/doc/282898>.

@article{DibyenduDe2008,
abstract = {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.},
author = {Dibyendu De, Neil Hindman, Dona Strauss},
journal = {Fundamenta Mathematicae},
keywords = {central sets theorem; Stone-Cech compactification of semigroups},
language = {eng},
number = {2},
pages = {155-175},
title = {A new and stronger central sets theorem},
url = {http://eudml.org/doc/282898},
volume = {199},
year = {2008},
}

TY - JOUR
AU - Dibyendu De
AU - Neil Hindman
AU - Dona Strauss
TI - A new and stronger central sets theorem
JO - Fundamenta Mathematicae
PY - 2008
VL - 199
IS - 2
SP - 155
EP - 175
AB - 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.
LA - eng
KW - central sets theorem; Stone-Cech compactification of semigroups
UR - http://eudml.org/doc/282898
ER -