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On weak and strong interpolation in algebraic logics

Published online by Cambridge University Press:  12 March 2014

Gábor Sági  and
Saharon Shelah
Gábor Sági
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest Pf. 127, H-1364, Hungary. E-mail: sagi@renyi.hu
Saharon Shelah
Affiliation:
Department of Mathematics, Hebrew University, 91904 Jerusalem, Israel. E-mail: shelah@math.huji.ac.il
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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].

Keywords

Key words and phrases. Craig InterpolationStrong AmalgamationSuperamalgamationVarieties of Cylindric Algebras
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 104 - 118
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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