On weak and strong interpolation in algebraic logics
Saharon Shelah and Gábor Sági
Source: J. Symbolic Logic Volume 71, Issue 1
(2006), 104-118.
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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Keywords: Craig Interpolation; Strong Amalgamation; Superamalgamation; Varieties of Cylindric Algebras
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1140641164
Digital Object Identifier: doi:10.2178/jsl/1140641164
Zentralblatt MATH identifier: 05038889
Mathematical Reviews number (MathSciNet): MR2210057
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