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Sets of ordinals constructible from trees and the third Victoria Delfino problem

Becker, Howard S. and Kechris, Alexander S. (1984) Sets of ordinals constructible from trees and the third Victoria Delfino problem. In: Axiomatic Set Theory. Contemporary Mathematics. No.31. American Mathematical Society , Providence, RI, pp. 13-29. ISBN 978-0-8218-5026-8. https://resolver.caltech.edu/CaltechAUTHORS:20130611-104220186

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Abstract

A very important part of the structure theory of Σ^1_2 sets of reals is based on their close interrelationship with the Gödel constructible universe L. The fundamental fact underlying this connection is the theorem of Shoenfield which asserts that every Σ^1_2 set of reals is Souslin over L. This means that given any Σ^1_2 subset of the reals (=ω^ω in this paper), there is a tree T on ω x λ (λ some ordinal, which can be taken to be ℵ_l here) such that T є L and A = p[T] = {ɑ є ω^ω: : ∃f є λ^ω ∀n(ɑ↾n,f↾n) є T}.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/conm/031DOIUNSPECIFIED
http://www.ams.org/books/conm/031/PublisherUNSPECIFIED
Additional Information:© 1984 American Mathematical Society. Research partially supported by NSF Grant MCS 82-11328. Research partially supported by NSF Grant MCS 81-17804.
Funders:
Funding AgencyGrant Number
NSFMCS 82-11328
NSFMCS 81-17804
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0763889
Series Name:Contemporary Mathematics
Issue or Number:31
Classification Code:1980 MSC Subject Classification: 03D70, 03E15, 03E45, 03E60, 04A15
Record Number:CaltechAUTHORS:20130611-104220186
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130611-104220186
Official Citation:Howard S. Becker and Alexander S. Kechris – Sets of ordinals constructible from trees and the third Victoria Delfino problem Pages 13-29
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38891
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 Jun 2013 20:11
Last Modified:03 Oct 2019 05:01

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