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A note on universal sets for classes of countable G_δ'S

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 . http://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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1112/S0025579300004484DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=6711888PublisherUNSPECIFIED
Additional Information:© 1975 University College London. Received June 27 1974. Published online: 26 February 2010.
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0420579
Record Number:CaltechAUTHORS:20130529-073254315
Persistent URL:http://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
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:31 May 2013 14:49
Last Modified:13 Feb 2019 18:05

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