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Stability and Categoricity of Lattices

Published online by Cambridge University Press:  20 November 2018

Kenneth W. Smith
Kenneth W. Smith*
Affiliation:
Logistics Department, Imperial Oil Limited, Toronto, Ontario
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This paper is a contribution to applied stability theory. Our purpose is to investigate the complexity of lattices by determining the stability of their first order theories.

Stability measures the complexity of a theory T by counting the number of different “kinds” of elements in models of T. The notion of ω-stability was introduced by Morley [26] in 1965 and generalized by Shelah [31] in 1969. Shelah classified all first order theories according to their stability properties.

Stability and -categoricity are closely related (see [26] and [1]). In fact, the notions of stable, superstable and ω-stable can be regarded as successive approximations of -categorical. -categoricity is a very strong property while stability, superstability and ω-stability facilitate the classification of more “complex” theories.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 6 , 01 December 1981 , pp. 1380 - 1419
Copyright
Copyright © Canadian Mathematical Society 1981

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