Optimal Proofs of Determinacy II

We present a general lemma which allows proving determinacy from Woodin cardinals. The lemma can be used in many different settings. As a particular application we prove the determinacy of sets in , n ≥ 1. The assumption we use to prove determinacy is optimal in the base theory of determinacy.

[1]  John R. Steel.  Inner Models with Many Woodin Cardinals , 1993, Ann. Pure Appl. Logic.

[2]  Leo Harrington,et al.  Analytic determinacy and 0# , 1978, Journal of Symbolic Logic.

[3]  Donald A. Matrin.  Measurable cardinals and analytic games , 1970 .

[4]  Donald A. Martin,et al.  The largest countable this, that, and the other , 1983 .

[5]  W H Woodin,et al.  Equivalence of partition properties and determinacy. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[6]  John R. Steel,et al.  A proof of projective determinacy , 1989 .

[7]  Itay Neeman.  Optimal proofs of determinacy , 1995, Bull. Symb. Log..