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Uncountable theories that are categorical in a higher power

Published online by Cambridge University Press:  12 March 2014

Michael Chris Laskowski
Michael Chris Laskowski*
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
*
Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
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Abstract

In this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime and minimal models over arbitrary base sets. The second theorem shows that such theories have a natural notion of dimension that determines the models of the theory up to isomorphism. From this we conclude that I(T,ℵα,) = ℵ0 + ∣α∣ where ℵα = the number of formulas modulo T-equivalence provided that T is not totally categorical. The third theorem gives a new characterization of these theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 512 - 530
Copyright
Copyright © Association for Symbolic Logic 1988

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References

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