Abstract
The projective sets constitute the traditional field of study in descriptive set theory, but they only form a part, albeit one that is very important, of the domain of “definable” sets in Polish spaces. In the last 25 years or so the range of classical descriptive set theory has been greatly expanded, under “Definable Determinacy”, to encompass vastly more extensive hierarchies of “definable sets”, such as, for example, those belonging to L(ℝ), that is, the smallest model of ZF set theory containing all the ordinals and reals. (The projective, the σ-projective, as well as the more complex hyperprojective sets belong to this model.) The reader can consult Y. N. Moschovakis [1980] and the seminar notes A. S. Kechris et al. [1978, 1981, 1983, 1988] on these developments.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Kechris, A.S. (1995). Epilogue. In: Classical Descriptive Set Theory. Graduate Texts in Mathematics, vol 156. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4190-4_40
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4190-4_40
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8692-9
Online ISBN: 978-1-4612-4190-4
eBook Packages: Springer Book Archive