Some remarks on uncountable rainbow Ramsey theory

2018/09/03 by Jing Zhang, Zhang, Jing
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1809.00649

Abstract

We discuss the rainbow Ramsey theorems at limit cardinals and successors of singular cardinals, addressing some questions in \citeMR2354904 and \citeMR2902230. In particular, we show for inaccessible κ, κ→^poly(κ)²_2-bdd does not characterize weak compactness and for singular κ, GCH+\square_κ implies κ⁺\not→^poly (η)²_

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