2023/03/14 by Ziemowit Kostana, Kostana, Ziemowit
Computer Science · Economics, Econometrics and Finance · Mathematics · #03E17 03E65 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2303.07694
openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study a family of axioms that closely follows the pattern of parametrized diamonds, studied by Moore, Hrušák, and Džamonja in [13]. However, our approach appeals to model theoretic / forcing theoretic notions, rather than pure combinatorics. The main goal of the paper is to exhibit a surprising, close connection between seemingly very distinct principles. As an application, we show that forcing with a measure algebra preserves (a variant of) \diamondsuit(\mathfrakd), improving an old result of M. Hrušák.