On weak and strong interpolation in algebraic logics

Gábor Sági; Saharon Shelah

doi:10.2178/jsl/1140641164

On weak and strong interpolation in algebraic logics

Gábor Sági^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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].

Original language	English
Pages (from-to)	104-118
Number of pages	15
Journal	Journal of Symbolic Logic
Volume	71
Issue number	1
DOIs	https://doi.org/10.2178/jsl/1140641164
State	Published - Mar 2006

Keywords

Craig Interpolation
Strong Amalgamation
Superamalgamation
Varieties of Cylindric Algebras

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On weak and strong interpolation in algebraic logics

Abstract

Keywords

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