Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T20:53:02.137Z Has data issue: false hasContentIssue false

Separation Principles and Bounded Quantification

Published online by Cambridge University Press:  20 November 2018

A. M. Dawes*
Affiliation:
The University of Western, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 SZ.

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
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