Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-05T18:49:23.151Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Devlin, K. J.Aspects of constructibility (Lecture Notes in Maths, no. 354, Springer-Verlag, 1973).CrossRefGoogle Scholar
(2)Drake, F. R.Set theory (North Holland, 1974).Google Scholar
(3)Jech, T. J.Lectures in set theory (Lecture Notes in Maths, no. 217, Springer-Verlag 1971).Google Scholar
(4)Kunen, K. and Tall, F. T. Between Martin's axiom and Souslin's hypothesis. (To appear.)Google Scholar
(5)Kukatowski, K.Ensembles projectifs et ensembles singuliers. Fund. Math. 35 (1948), 131–140.CrossRefGoogle Scholar
(6)Kuratowski, K.Topology, vol. I, translated from the French edition by J. Jaworoski (New York, London: Academic Press, 1966).Google Scholar
(7)Martin, D. A. and Solovay, R. M.Internal Cohen Extensions. Ann. of Math. Logic 2 (1970), 143–178.CrossRefGoogle Scholar
(8)Shoenfield, J. R.Mathematical logic (Addison Wesley, 1967).Google Scholar
(9)Solovay, R. M. On the cardinality of sets of reals, in Foundations of mathematics, Symposium Papers commemorating the Sixtieth Birthday of Kurt Gödel, ed. Bulloff, J. J.et al., pp. 58–73 (Berlin, Springer-Verlag, 1969).CrossRefGoogle Scholar