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On the existence of an analytic set meeting each compact set in a Borel set

Published online by Cambridge University Press:  24 October 2008

A. R. D. Mathias ,
A. J. Ostaszewski  and
M. Talagrand
A. R. D. Mathias
Affiliation:
Peterhouse, Cambridge, Université Paris VI, 4 Place Jussieu, 75230 Paris
A. J. Ostaszewski
Affiliation:
London School of Economics, Université Paris VI, 4 Place Jussieu, 75230 Paris
M. Talagrand
Affiliation:
Equipe d'Analyse, Université Paris VI, 4 Place Jussieu, 75230 Paris
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Extract

C. A. Rogers and J. E. Jayne have asked whether, given a Polish space and an analytic subset A of which is not a Borel set, there is always a compact subset K of such that, A ∩ K is not Borel. In this paper we give both a proof, using Martin's axiom and the negation of the continuum hypothesis, of and a counter-example, using the axiom of constructibility, to the conjecture of Rogers and Jayne, which set theory with the axiom of choice is thus powerless to decide.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 5 - 10
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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