Structural Consequences of AD

Steve Jackson ()
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Steve Jackson: University of North Texas, Department of Mathematics

Chapter 21 in Handbook of Set Theory, 2010, pp 1753-1876 from Springer

Abstract: 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: Scale Property; Winning Strategy; Homogeneous Tree; Countable Union; Regular Cardinal (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4020-5764-9_22

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