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Six classes of theories*

Published online by Cambridge University Press:  09 April 2009

H. Jerome Keisler
H. Jerome Keisler
Affiliation:
Mathematics Department, University of Wisconsin, Van Vleck Hall 480 Lincoln Drive Madison, Wisconsin 53706, U.S.A.
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A theory T is said to κ-stable if, given a pair of models U ⊂ B of T with U of power κ, there are only κ types of elements of B over U (types are defined below). This notion was introduced by Morley (1965) who gave a powerful analysis of ω-stable theories. Shelah (1971) showed that there are only four possibilities for the set of κ in which a countable theory is stable. This partition of all theories into four classes (ω-stable, superstable, stable, and unstable theories) has proved to be of great value. However, most familiar examples of theories are unstable.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 257 - 266
Copyright
Copyright © Australian Mathematical Society 1976

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