Higherdimensional Deltasystems
Abstract
We investigate higherdimensional $\Delta$systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higherdimensional version of the classical $\Delta$system lemma. We focus in particular on systems that consist of sets of ordinals, in which case useful ordertheoretic uniformities can be ensured. We then present three applications of these higherdimensional $\Delta$systems to problems involving the interplay between forcing and partition relations on the reals.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.01086
 arXiv:
 arXiv:2006.01086
 Bibcode:
 2020arXiv200601086L
 Keywords:

 Mathematics  Logic;
 03E05;
 03E02;
 03E35
 EPrint:
 24 pages