Kechris, A. S. and Martin, D. A.
(1975)
*A note on universal sets for classes of countable G_δ'S.*
Mathematika, 22
(1).
pp. 43-45.
ISSN 0025-5793 .
https://resolver.caltech.edu/CaltechAUTHORS:20130529-073254315

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## Abstract

In a recent article [2] D. G. Larman and C. A. Rogers proved the following two results in Descriptive Set Theory (where R = the space of real numbers): (1) There is no analytic set in the plane R^2, which is universal for the countable closed subsets of R; (2) there is no Borel set in R^2, which is universal for the countable G_δ subsets of R. Recall that, if b is a class of subsets of a space X, a set U ⊆ X × X is called universal for C if (ɑ) for each x є X, U_x = def {y : (x, y) U} є C, and (b) for each A є C there is an x such that A = U_x. (Larman and Rogers have also shown that in both cases coanalytic universal sets exist.)

Item Type: | Article | |||||||||
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Additional Information: | © 1975 University College London. Received June 27 1974. Published online: 26 February 2010. | |||||||||

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Issue or Number: | 1 | |||||||||

Record Number: | CaltechAUTHORS:20130529-073254315 | |||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130529-073254315 | |||||||||

Official Citation: | A. S. Kechris and D. A. Martin (1975). A note on universal sets for classes of countable Gδ'S. Mathematika, 22, pp 43-45. doi:10.1112/S0025579300004484. | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 38699 | |||||||||

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Deposited By: | Ruth Sustaita | |||||||||

Deposited On: | 31 May 2013 14:49 | |||||||||

Last Modified: | 03 Oct 2019 04:59 |

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