Abstract
We study and clarify the close connection between ideals determined by unsymmetric games, the combinatorial notion of constant prediction, and the concept of strong porosity. We obtain a number of new results, mostly in ZFC, about cardinal invariants related to these notions. Our results answer questions of Newelski and Roslanowski (Proc Amer Math Soc 117(3):823–831, 1993, Problem 3.6), of Kamo (J Math Soc Japan 53(1):35–57, 2001, Question 2), of Brendle and Shelah (Arch Math Logic 42(4):349–360, 2003, Questions 3.11 and 3.12), and of Guzman et al. (J Log Anal 9(6), 2017, Questions 5.2, 5.3, 5.4, and 5.5).
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