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On weak and strong interpolation in algebraic logics

Published online by Cambridge University Press:  12 March 2014

Gábor Sági
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest Pf. 127, H-1364, Hungary. E-mail:
Saharon Shelah
Department of Mathematics, Hebrew University, 91904 Jerusalem, Israel. E-mail:


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].

Research Article
Copyright © Association for Symbolic Logic 2006

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