On Weak and Strong Interpolation in Algebraic Logics

Journal of Symbolic Logic 71 (1):104 - 118 (2006)
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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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Citations of this work

Interpolation property and homogeneous structures.Z. Gyenis - 2014 - Logic Journal of the IGPL 22 (4):597-607.
Three interpolation theorems for typeless logics.T. Sayed Ahmed - 2012 - Logic Journal of the IGPL 20 (6):1001-1037.
The Robinson property and amalgamations of higher arities.David Nyiri - 2016 - Mathematical Logic Quarterly 62 (4-5):427-433.
Varying interpolation and amalgamation in polyadic MV-algebras.Tarek Sayed Ahmed - 2015 - Journal of Applied Non-Classical Logics 25 (2):140-192.

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.

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