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March 2006 On weak and strong interpolation in algebraic logics
Saharon Shelah, Gábor Sági
J. Symbolic Logic 71(1): 104-118 (March 2006). DOI: 10.2178/jsl/1140641164

Abstract

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig’s Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].

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Saharon Shelah. Gábor Sági. "On weak and strong interpolation in algebraic logics." J. Symbolic Logic 71 (1) 104 - 118, March 2006. https://doi.org/10.2178/jsl/1140641164

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1100.03021
MathSciNet: MR2210057
Digital Object Identifier: 10.2178/jsl/1140641164

Subjects:
Primary: 03C40, 03G15

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 1 • March 2006
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