Vol. 60, No. 1, 1975

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ISSN: 0030-8730
Countable ordinals and the analytical hierarchy. I

Alexander S. Kechris

Vol. 60 (1975), No. 1, 223–227
Abstract

The following results are proved, using the axiom of Projective Determinacy: (i) For n 1, every Π2n+11 set of countable ordinals contains a Δ2n+11 ordinal, (ii) For n 1, the set of reals Δ2n1 in an ordinal is equal to the largest countable Σ2n1 set and (iii) Every real is Δn1 inside some transitive model of set theory if and only if n 4.

Mathematical Subject Classification
Primary: 02K30
Secondary: 02K15, 02K05
Milestones
Received: 29 August 1974
Published: 1 September 1975
Authors
Alexander S. Kechris
Department of Mathematics
California Institute of Technology
253-37
Pasadena CA 91125-0001
United States
http://www.math.caltech.edu/people/kechris.html