Harrington, Leo and Kechris, Alexander S. (1977) ∏^1_2 singletons and O^#. Fundamenta Mathematicae, 95 (3). pp. 167-171. ISSN 0016-2736. https://resolver.caltech.edu/CaltechAUTHORS:20130528-111450945
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Abstract
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 | ||||
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| Additional Information: | © 1977. Accepté par la Rèdaction le 1.4.1975. | ||||
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| Issue or Number: | 3 | ||||
| Record Number: | CaltechAUTHORS:20130528-111450945 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130528-111450945 | ||||
| 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 | ||||
| Collection: | CaltechAUTHORS | ||||
| Deposited By: | Ruth Sustaita | ||||
| Deposited On: | 30 May 2013 17:21 | ||||
| Last Modified: | 03 Oct 2019 04:59 |
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