Structural Consequences of AD
- Steve JacksonAffiliated withDepartment of Mathematics, University of North Texas Email author
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.
- Structural Consequences of AD
- Book Title
- Handbook of Set Theory
- pp 1753-1876
- Print ISBN
- Online ISBN
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media B.V.
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- Editor Affiliations
- ID1. School of Physical Sciences, University of California, Irvine
- ID2. Dept. Manufacturing Engineering, Boston University
- Steve Jackson (1)
- Author Affiliations
- 1. Department of Mathematics, University of North Texas, Denton, TX, 76203, USA
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