2020/06/01 by Lambie-Hanson, Chris
#03E02 #03E05 #03E35 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2006.01086
We investigate higher-dimensional Δ-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical Δ-system lemma. We focus in particular on systems that consist of sets of ordinals, in which case useful order-theoretic uniformities can be ensured. We then present three applications of these higher-dimensional Δ-systems to problems involving the interplay between forcing and partition relations on the reals.