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Separation Principles and Bounded Quantification

Published online by Cambridge University Press:  20 November 2018

A. M. Dawes
A. M. Dawes*
Affiliation:
The University of Western, Ontario
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This note is concerned with the implication SepII(Q)→SepI(Q) where Q is a class of subsets of some set S.

where cZ denotes S—Z.

It is well-known that in general the above implication is false (e.g. let Q be the closed subsets of the reals).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 295 - 296
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Addison, J. W., Separation principles in the hierarchies of classical and effective descriptive set theory. Fundamenta Mathematicae XLVI (1958) pp. 123-135.Google Scholar
2. Dawes, A. M., First-order hierarchies in general models and in models of Peano arithmetic. Ph.D. thesis, University of Toronto, Toronto, 1972.Google Scholar