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Published July 2017 | Submitted
Journal Article Open

Gowers' Ramsey Theorem for generalized tetris operations

Abstract

We prove a generalization of Gowers' theorem for FIN_k where, instead of the single tetris operation T:FIN_k→FIN_(k−1), one considers all maps from FIN_k to FIN_j for 0≤j≤k arising from nondecreasing surjections f:{0,1,…,k}→{0,1,…,j}. This answers a question of Bartošová and Kwiatkowska. We also describe how to prove a common generalization of such a result and the Galvin–Glazer–Hindman theorem on finite products, in the setting of layered partial semigroups introduced by Farah, Hindman, and McLeod.

Additional Information

© 2017 Elsevier Inc. Received 6 April 2016, Available online 20 February 2017. We are grateful to David Fernandez, Aleksandra Kwiatkowska, Sławomir Solecki, and Kostas Tyros for their comment and suggestions. We are also thank Aleksandra Kwiatkowska for pointing out a mistake in an earlier version of this paper, and Ilijas Farah for referring us to [3] and to the theory of layered partial semigroups.

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August 21, 2023
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