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PRIMITIVE RECURSIVE BOUNDS FOR THE FINITE VERSION OF GOWERS’ $c_{0}$ THEOREM

Part of: Extremal combinatorics

Published online by Cambridge University Press:  07 January 2015

Konstantinos Tyros
Konstantinos Tyros*
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. email [email protected]
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Abstract

We provide primitive recursive bounds for the finite version of Gowers’ $c_{0}$ theorem for both the positive and the general case. We also provide multidimensional versions of these results.

MSC classification

Primary: 05D10: Ramsey theory
Type
Research Article
Information
Mathematika , Volume 61 , Issue 3 , September 2015 , pp. 501 - 522
Copyright
Copyright © University College London 2015 

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References

Benyamini, Y. and Lindenstrauss, J., Geometric Nonlinear Functional Analysis, Vol. 1 (American Mathematical Society Colloquium Publications 48), American Mathematical Society (Providence, RI, 2000).Google Scholar
Dodos, P. and Kanellopoulos, V., Topics in Ramsey Theory. Preprint.Google Scholar
Erdős, P. and Rado, R., Combinatorial theorems on classifications of subsets of a given set. Proc. Lond. Math. Soc. (3) 2 1952, 417–439.CrossRefGoogle Scholar
Gowers, W. T., Lipschitz functions on classical spaces. European J. Combin. 13 1992, 141–151.CrossRefGoogle Scholar
Gowers, W. T., Ramsey methods in Banach spaces. In Handbook of the Geometry of Banach Spaces, Vol. 2 (eds Johnson, W. B. and Lindenstrauss, J.), Elsevier (Amsterdam, 2003), 1071–1097.CrossRefGoogle Scholar
Graham, R. L. and Rothschild, B. L., Ramsey’s theorem for n-parameter sets. Trans. Amer. Math. Soc. 159 1971, 257–292.Google Scholar
Hindman, N., Finite sums from sequences within cells of a partition of ℕ. J. Combin. Theory Ser. A 17 1974, 1–11.CrossRefGoogle Scholar
Kanellopoulos, V., A proof of W. T. Gowers’ c 0 theorem. Proc. Amer. Math. Soc. 132(11) 2004, 3231–3242 (electronic).CrossRefGoogle Scholar
Kechris, A. S., Pestov, V. G. and Todorcevic, S., Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups. Geom. Funct. Anal. 15(1) 2005, 106–189.CrossRefGoogle Scholar
Milliken, K., Ramsey’s theorem with sums or unions. J. Combin. Theory Ser. A 18 1975, 276–290.CrossRefGoogle Scholar
Ojeda-Aristizabal, D., Finite forms of Gowers’ theorem on the oscillation stability of $c_{0}$. Preprint, 2013, arXiv:1312.4639 [math.CO].Google Scholar
Rose, H. E., Subrecursion: Functions and Hierarchies (Oxford Logic Guide 9), Oxford University Press (Oxford, 1984).Google Scholar
Shelah, S., Primitive recursive bounds for van der Waerden numbers. J. Amer. Math. Soc. 1 1988, 683–697.CrossRefGoogle Scholar
Taylor, A. D., A canonical partition relation for the finite subsets of 𝜔. J. Combin. Theory Ser. A 21 1976, 137–146.CrossRefGoogle Scholar
Taylor, A. D., Bounds for the disjoint unions theorem. J. Combin. Theory Ser. A 30 1981, 339–344.CrossRefGoogle Scholar
Todorcevic, S., Introduction to Ramsey Spaces (Annals of Mathematics Studies 174), Princeton University Press (Princeton, NJ, 2010).CrossRefGoogle Scholar