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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Nonmetrizable topological dynamics and Ramsey theory


Authors: Vitaly Bergelson and Neil Hindman
Journal: Trans. Amer. Math. Soc. 320 (1990), 293-320
MSC: Primary 03E05; Secondary 05A17, 54A25, 54H20
DOI: https://doi.org/10.1090/S0002-9947-1990-0982232-5
MathSciNet review: 982232
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Abstract: Applying ideas from topological dynamics in compact metric spaces to the Stone-Cěch compactification of a discrete semigroup, several new proofs of old results and some new results in Ramsey Theory are obtained. In particular, two ultrafilter proofs of van der Waerden's Theorem are given. An ultrafilter approach to "central" sets (sets which are combinatorially rich) is developed. This enables us to show that for any partition of the positive integers one cell is both additively and multiplicatively central. Also, a fortuitous answer to a question of Ellis is obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0982232-5
Keywords: Ramsey Theory, van der Waerden's Theorem, central sets
Article copyright: © Copyright 1990 American Mathematical Society