On Weak and Strong Interpolation in Algebraic Logics

Journal of Symbolic Logic 71 (1):104 - 118 (2006)
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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DOI 10.2178/jsl/1140641164
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Interpolation Property and Homogeneous Structures.Z. Gyenis - 2014 - Logic Journal of the IGPL 22 (4):597-607.

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