Journal of Symbolic Logic

Rich Models

Michael H. Albert and Rami P. Grossberg

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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 $\min(2^\lambda,\beth_2)$ 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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743420

Mathematical Reviews number (MathSciNet)
MR1071329

Zentralblatt MATH identifier
0721.03021

JSTOR
links.jstor.org

Citation

Albert, Michael H.; Grossberg, Rami P. Rich Models. J. Symbolic Logic 55 (1990), no. 3, 1292--1298. https://projecteuclid.org/euclid.jsl/1183743420


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