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Theory of models with generalized atomic formulas

Published online by Cambridge University Press:  12 March 2014

H. Jerome Keisler
H. Jerome Keisler*
Affiliation:
California Institute of Technology
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Introduction

We shall prove the following theorem, which gives a necessary and sufficient condition for an elementary class to be characterized by a set of sentences having a prescribed number of alternations of quantifiers. A finite sequence of relational systems is said to be a sandwich of order n if each is an elementary extension of (i ≦ n—2), and each is an extension of (i ≦ n—2). If K is an elementary class, then the statements (i) and (ii) are equivalent for each fixed natural number n.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 1 , March 1960 , pp. 1 - 26
Copyright
Copyright © Association for Symbolic Logic 1960

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