Vol. 60, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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