Baire sets of 𝑘-parameter words are Ramsey

Prömel, Hans Jürgen; Voigt, Bernd

doi:10.1090/S0002-9947-1985-0797054-6

Baire sets of $k$-parameter words are Ramsey
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by Hans Jürgen Prömel and Bernd Voigt PDF

Trans. Amer. Math. Soc. 291 (1985), 189-201 Request permission

Abstract:

We show that Baire sets of $k$-parameter words are Ramsey. This extends a result of Carlson and Simpson, A dual form of Ramsey’s theorem, Adv. in Math. 53 (1984), 265-290. Employing the method established therefore, we derive analogous results for Dowling lattices and for ascending $k$-parameter words.

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CS84

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In these notes I give

A dual form of Erdös-Rado’s canonization theorem

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Parameter words, trees and vector spaces