Structural Consequences of AD

Chapter

Abstract

In this chapter we survey recent advances in descriptive set theory, starting (roughly) from where Moschovakis’ book (1980) ends. Our survey is not intended to be complete, but focuses mainly on the structural consequences of determinacy for the model L(ℝ), including the important case of the projective sets. By “structural” we are referring to the combinatorial theory of the pointclasses (for example, the scale property which in some sense describes the structure of the set) as well as the cardinal structure up to the natural ordinal associated with these pointclasses. This might include determining their cofinalities, partition properties, and so forth.

Keywords

Hull Boulder Alexan 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North TexasDentonUSA

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