Determinacy Transfer for sigma-Projective Sets of Reals

(with J. Aguilera and P. Schlicht)

Determinacy transfer theorems play an important role in the descriptive set theoretic and inner model theoretic study of pointclasses. We prove that determinacy for $\sigma$-projective sets, a natural generalization of projective sets to a $\sigma$-algebra, of length $\omega$ implies the determinacy of a large class of games of length $\omega^2$. The proof of this result involves inner models with large cardinals and in the process, we obtain a new proof of $\sigma$-projective determinacy for games of countable length from the existence of inner models with large cardinals.

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