Determinacy in the difference hierarchy of co-analytic sets
It is shown for recursive ordinals \(\alpha\) that \(\omega^2\alpha- \Pi^1_1\) determinacy is equivalent to existence of a clever \(\alpha\)-mouse. It is also shown for every countable ordinal \(\delta\) that if there is a sequence \(\langle \kappa_i: i< \delta+ 1\rangle\) of measurable cardinals and an almost \(< \omega_1\)-Erdös cardinal above them, then \(\omega^2(\delta+ 1)- \Pi^1_1\) determinacy holds. It is also shown that if the Weak Chang Conjecture holds at \(\omega_1\), then \(\omega^2- \Pi^1_1\) determinacy holds.
scientific article; zbMATH DE number 908481
scientific article