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Some useful preservation theorems

Published online by Cambridge University Press:  12 March 2014

Kevin J. Compton
Kevin J. Compton*
Affiliation:
Wesleyan University, Middletown, Connecticut 06457
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Extract

The study of preservation theorems for first order logic was the focus of much research by model theorists in the 1960's. These theorems, which came to form the foundation for classical model theory, characterize first order sentences and theories that are preserved under operations such as the taking of unions or submodels (see Chang and Keisler [5] for a discussion of preservation theorems for first order logic). In current model theoretic research, logics richer than first order logic and applications of logic to other parts of mathematics have assumed the central position. In the former area, preservation theorems are not so important; in the latter, especially in applications to algebra, many of the techniques developed for proving these theorems have been useful.

In this paper I prove several preservation theorems for first order logic which I discovered while investigating the asymptotic growth of classes of finite combinatorial structures. The significance of these theorems lies in their applications to problems in finite combinatorics. Since the applications require combinatorial and analytical techniques that are not pertinent to logical questions discussed here, I shall present them in another paper [7].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 2 , June 1983 , pp. 427 - 440
Copyright
Copyright © Association for Symbolic Logic 1983

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References

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