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
|
PDF
- Published Version
See Usage Policy. 183kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20130528-081912845
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 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Related URLs: |
| |||||||||
Additional Information: | © 1979, Association for Symbolic Logic. Received November 15, 1976. Research partially supported by NSF Grant MPS75-07562. | |||||||||
Funders: |
| |||||||||
Other Numbering System: |
| |||||||||
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 |
Repository Staff Only: item control page