Journal of Symbolic Logic

Rich Models

Michael H. Albert and Rami P. Grossberg

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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 $\min(2^\lambda,\beth_2)$ rich models of cardinality $\lambda(\lambda > |T|)$ is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in $\aleph_1$ and also has a unique countable rich model. We also consider a stronger notion of richness, and use it to characterize superstable theories.

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J. Symbolic Logic, Volume 55, Issue 3 (1990), 1292-1298.

First available in Project Euclid: 6 July 2007

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Albert, Michael H.; Grossberg, Rami P. Rich Models. J. Symbolic Logic 55 (1990), no. 3, 1292--1298.

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