Gowers' Ramsey Theorem for generalized tetris operations

摘要

We prove a generalization of Cowers' theorem for FIN kappa where, instead of the single tetris operation T : FINk -> FINk-1, one considers all maps from FINk to FINj for 0 <= j <= k arising from nondecreasing surjections f : {0, 1,..., k} --+ {0,1,..., j}. This answers a question of Bartogova 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. (C) 2017 Elsevier Inc. All rights reserved.