Projectively Well-Ordered Inner Models

@article{Steel1995ProjectivelyWI,
  title={Projectively Well-Ordered Inner Models},
  author={John R. Steel},
  journal={Ann. Pure Appl. Logic},
  year={1995},
  volume={74},
  pages={77-104}
}
We show that the reals in the minimal iterable inner model having n Woodin cardinals are precisely those which are A,‘+ 2 definable from some countable ordinal. (One direction here is due to Hugh Woodin.) It follows that this model satisfies “There is a A.‘+2 well-order of the reals”. We also describe some other connections between the descriptive set theory of projective sets and inner models with finitely many Woodin cardinals. 

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Kechris , Measure and category m effective descriptive set theory

D. A. Martin Kechris, R. M. Solovay
Ann . Math . Logic • 1973

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