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.
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© 1995 Springer-Verlag New York, Inc.
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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
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DOI: https://doi.org/10.1007/978-1-4612-4190-4_40
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