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Rich models

Published online by Cambridge University Press:  12 March 2014

Michael H. Albert  and
Rami P. Grossberg
Michael H. Albert
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Rami P. Grossberg
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
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Abstract

We define a rich model to be one which contains a proper elementary substructure isomorphic to itself. Existence, nonstructure, and categoricity theorems for rich models are proved. A theory T which has fewer than min(2λ, ℶ2) rich models of cardinality λ (λ > ∣T∣) is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in ℵ1 and also has a unique countable rich model. We also consider a stronger notion of richness, and use it to characterize superstable theories.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 1292 - 1298
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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