Local Ramsey Spaces in Matet Forcing Extensions and Finitely Many\n Near-Coherence Classes

2014/04/29 by Heike Mildenberger, Mildenberger, Heike
Computer Science · Mathematics · #03E05 #03E35 #05C55 #05D10 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Limits and Structures in Graph Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1404.7350

openalex publication_date 2014/04/29 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We introduce Gowers--Matet forcing with a finite sequence of pairwise\nnon-isomorphic Ramsey ultrafilters over \ω, and with this forcing we\nsettle the long-standing problem of the spectrum of numbers near-coherence\nclasses. We prove that for any finite n \≥ 1, there is a forcing extension\nwith exactly n near-coherence classes of ultrafilters.\n For evaluating the new forcing, we prove a strengthening of Gowers's theorem\non colourings of rm Fin_k.\n

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