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The Theory of Countable Analytical Sets

Kechris, Alexander S. (1975) The Theory of Countable Analytical Sets. Transactions of the American Mathematical Society, 202 (2). pp. 259-297. ISSN 0002-9947.

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The purpose of this paper is the study of the structure of countable sets in the various levels of the analytical hierarchy of sets of reals. It is first shown that, assuming projective determinacy, there is for each odd n a largest countable ∏_n^1 set of reals, C_n (this is also true for n even, replacing ∏_n^1 by Σ_n^1 and has been established earlier by Solovay for n = 2 and by Moschovakis and the author for all even n > 2). The internal structure of the sets C_n is then investigated in detail, the point of departure being the fact that each C_n is a set of Δ_n^1-degrees, wellordered under their usual partial ordering. Finally, a number of applications of the preceding theory is presented, covering a variety of topics such as specification of bases, ω-models of analysis, higher-level analogs of the constructible universe, inductive definability, etc.

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Additional Information:© 1975 American Mathematical Society. Received by the editors September 13, 1973. Research partially supported by NSF grant GP 27964.
Funding AgencyGrant Number
NSFGP 27964
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0419235
Issue or Number:2
Classification Code:AMS (MOS) subject classifications (1970). Primary 04A15, 02K30, 28A05, 54H05; Secondary 02F35, 02K05, 02K25, 02K35, 04A30.
Record Number:CaltechAUTHORS:20130522-132343731
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Official Citation:The theory of countable analytical sets Alexander S. Kechris. Trans. Amer. Math. Soc. 202 (1975), 259-297
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38637
Deposited By: Ruth Sustaita
Deposited On:22 May 2013 20:52
Last Modified:03 Oct 2019 04:59

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