Kechris, Alexander S. (1978) The Perfect Set Theorem and Definable Wellorderings of the Continuum. Journal of Symbolic Logic, 43 (4). pp. 630-634. ISSN 0022-4812. https://resolver.caltech.edu/CaltechAUTHORS:20130528-081912845
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Abstract
Let Γ be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for Γ if every set in Γ with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on Γ and M): If M is a perfect set basis for Γ, the field of every wellordering in Γ is contained in M. An immediate corollary is Mansfield's Theorem that the existence of a Σ^1_2 wellordering of the reals implies that every real is constructible. Other applications and extensions of the main result are also given.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1979, Association for Symbolic Logic. Received November 15, 1976. Research partially supported by NSF Grant MPS75-07562. | |||||||||
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| Issue or Number: | 4 | |||||||||
| Record Number: | CaltechAUTHORS:20130528-081912845 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130528-081912845 | |||||||||
| Official Citation: | The Perfect Set Theorem and Definable Wellorderings of the Continuum Alexander S. Kechris; 630-634 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 38673 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 28 May 2013 15:34 | |||||||||
| Last Modified: | 03 Oct 2019 04:59 |
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