More on Cichoń's diagram and infinite games (Q2710603)

The author introduces some sorts of infinite games of two players on a~given cardinal~\(\kappa\) (cut-and-choose game, \(\mathcal G_{\mathfrak b}(\kappa)\), \(\mathcal G_{\mathfrak d}(\kappa)\)), and infinite games for subsets of~\(\omega^\omega\) (integer-valued sequence games). He uses them to characterize the cardinal invariants \(\text{cov}(\mathcal M)\), \(\text{non}(\mathcal M)\), \(\mathfrak b\), \(\mathfrak d\), \(\text{add}(\mathcal N)\), and \(\text{cof}(\mathcal N)\) (\(\mathcal M\) and \(\mathcal N\) denote the ideal of meager sets and the ideal of null sets, respectively). Modifications of some of the above games for forcing notions he uses to characterize Sacks property, \(\omega^\omega\)-bounding property, and Laver property.