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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.

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The following results are proved, using the axiom of Projective Determinacy: (i) For n ≥ 1, every II(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.

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Additional Information:© 1975 Pacific Journal of Mathematics. Received August 29, 1974. Research partially supported by NSF grant GP 27964.
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MathSciNet ReviewMR0387053
Issue or Number:1
Record Number:CaltechAUTHORS:KECpjm75
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:841
Deposited By: Tony Diaz
Deposited On:19 Oct 2005
Last Modified:02 Oct 2019 22:37

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