2007/06/26 by James Hirschorn, Hirschorn, James · 1 citation
Computer Science · Mathematics · #03E05 (Primary) #03E35 #03E50 #06A06 #91A46 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #math.LO #msc:03E05 #msc:03E35 #msc:03E50 #msc:06A06 #msc:91A46
paper · pdf · doi:10.48550/arxiv.0706.3729
1) Minor revisions. 2) Sharpened results by replacing the notion of a "global strategy" (see Definition 2.9)
openalex publication_date 2007/06/26 · arxiv created 2008/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider strong combinatorial principles for sigma-directed families of countable sets in the ordering by inclusion modulo finite, e.g. P-ideals of countable sets. We try for principles as strong as possible while remaining compatible with CH, and we also consider principles compatible with the existence of nonspecial Aronszajn trees. The main thrust is towards abstract principles with game theoretic formulations. Some of these principles are purely combinatorial, while the ultimate principles are primarily combinatorial but also have aspects of forcing axioms.