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∏^1_2 singletons and O^#

Harrington, Leo and Kechris, Alexander S. (1977) ∏^1_2 singletons and O^#. Fundamenta Mathematicae, 95 (3). pp. 167-171. ISSN 0016-2736.

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A conjecture of Solovay states: Assuming that for every real ɑ, ɑ^# exists, the constructibility degrees of ∏^1_2 singletons are wellordered and the successor steps in this wellordering are given by the sharps. In this paper we prove among others things that (assuming ∀ɑ (ɑ^# exists)) for every ∏^1_2 singleton a either O^# is constructible from ɑ or ɑ^# is constructible from O^#. From a relativized version of this result it follows that the constructibility degrees of O^#, O^(##), O^(###),... are the first ω constructibility degrees of sharps of ∏^1_2 singletons.

Item Type:Article
Additional Information:© 1977. Accepté par la Rèdaction le 1.4.1975.
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0460121
Issue or Number:3
Record Number:CaltechAUTHORS:20130528-111450945
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Official Citation:∏^1_2 singletons and O^# Leo Harrington, Alexander S. Kechris Fund. Math. 95 (1977), 167-171
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38692
Deposited By: Ruth Sustaita
Deposited On:30 May 2013 17:21
Last Modified:03 Oct 2019 04:59

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