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Minimum models of analysis1

Published online by Cambridge University Press:  12 March 2014

J. R. Shilleto
J. R. Shilleto*
Affiliation:
University of Saskatchewan, Regina, Canada
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Extract

Although there is no smallest ω model [6], Putnam and Gandy independently proved about 1963 that the class of ramified analytical sets, as defined by Cohen [3], form the smallest β model of analysis [2], [8]. This paper will consider other restricted classes of models, namely the βn models for integers n > 1 [10], and prove under appropriate assumptions the existence of minimum such models. In fact we shall construct the minimum βn model in a fashion similar to the procedure yielding the class of ramified analytical sets, but adding at each stage a segment of the sets in those already obtained (for n a fixed integer > 1).

Roughly speaking a βn model is an ω model absolute for n-set-quantifier assertions about its subsets of natural numbers. A β model is simply a β1 model. See Enderton and Friedman [4] for a further investigation of βn models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 37 , Issue 1 , March 1972 , pp. 48 - 54
Copyright
Copyright © Association for Symbolic Logic 1972

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Footnotes

1

This paper presents the work of the author's doctoral dissertation submitted to the University of California at Berkeley in February 1969.

References

BIBLIOGRAPHY

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