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Coinductive formulas and a many-sorted interpolation theorem

Published online by Cambridge University Press:  12 March 2014

Ursula Gropp
Ursula Gropp*
Affiliation:
Mathematisches Institut, Universität Bonn, Bonn, West Germany
*
Equipe de Logique Mathématique, Université Paris-vii, 75251 Paris, France
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Abstract

We use connections between conjunctive game formulas and the theory of inductive definitions to define the notions of a coinductive formula and its approximations. Corresponding to the theory of conjunctive game formulas we develop a theory of coinductive formulas, including a covering theorem and a normal form theorem for many sorted languages. Applying both theorems and the results on “model interpolation” obtained in this paper, we prove a many-sorted interpolation theorem for ω1ω-logic, which considers interpolation with respect to the language symbols, the quantifiers, the identity, and countably infinite conjunction and disjunction.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 3 , September 1988 , pp. 937 - 960
Copyright
Copyright © Association for Symbolic Logic 1988

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