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On strongly minimal sets

Published online by Cambridge University Press:  12 March 2014

J. T. Baldwin  and
A. H. Lachlan
J. T. Baldwin
Affiliation:
Simon Fraser University, Burnaby 2, British Columbia
A. H. Lachlan
Affiliation:
Simon Fraser University, Burnaby 2, British Columbia
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Extract

The purpose of this paper is twofold. In §1 and §2 which are largely expository we develop the known theory of ℵ1-categoricity in terms of strongly minimal sets. In §3 we settle affirmatively Vaught's conjecture that a complete ℵ1-categorical theory has either just one or just ℵ0 countable models, and in §4 we present an example which serves to illustrate the ideas of §3.

As far as we know the only work published on strongly minimal sets is that of Marsh [3]. The present exposition goes beyond [3] in showing that any ℵ-categorical theory has a principal extension in which some formula is strongly minimal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 1 , March 1971 , pp. 79 - 96
Copyright
Copyright © Association for Symbolic Logic 1971

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References

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