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Countable ordinals and the analytical hierarchy. I.

Kechris, A. S. (1975) Countable ordinals and the analytical hierarchy. I. Pacific Journal of Mathematics, 60 (1). pp. 223-227. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:20130612-115543154

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Abstract

The following results are proved, using the axiom of Projective Determinacy: (i) For n ⪴ 1, every ∏^1_(2n+1) set of countable ordinals contains a Δ^1_(2n+1) ordinal, (ii) For n ⪴ 1, the set of reals Δ^1_(2n) in an ordinal is equal to the largest countable Σ^1_(2n) set and (iii) Every real is Δ^1_n inside some transitive model of set theory if and only if n ⪴ 4.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/euclid.pjm/1102868636PublisherUNSPECIFIED
Additional Information:© 1975 Pacific Journal of Mathematics. Received August 29, 1974. Research partially supported by NSF grant GP 27964.
Funders:
Funding AgencyGrant Number
NSFGP 27964
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0387053
Zentralblatt MATH identifier0308.02062
Zentralblatt MATH identifier0287.02042
Classification Code:MCS: Primary Subjects: 02K30; Secondary Subjects: 02K05, 02K15
Record Number:CaltechAUTHORS:20130612-115543154
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130612-115543154
Official Citation:Countable ordinals and the analytical hierarchy. I. A. S. Kechris; 223-227
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38919
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2013 20:30
Last Modified:13 Feb 2019 18:05

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