Journal of Symbolic Logic

On weak and strong interpolation in algebraic logics

Saharon Shelah and Gábor Sági

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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].

Article information

J. Symbolic Logic, Volume 71, Issue 1 (2006), 104-118.

First available in Project Euclid: 22 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C40: Interpolation, preservation, definability 03G15: Cylindric and polyadic algebras; relation algebras

Craig Interpolation Strong Amalgamation Superamalgamation Varieties of Cylindric Algebras


Sági, Gábor; Shelah, Saharon. On weak and strong interpolation in algebraic logics. J. Symbolic Logic 71 (2006), no. 1, 104--118. doi:10.2178/jsl/1140641164.

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