On weak and strong interpolation in algebraic logics

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]. AMS Classification: 03C40, 03G15.

• Type: Journal
• Year: 2006
• Where: JSYML
• Authors: Saharon Shelah, Gábor Sági
• Keywords: First Order Logic, JSYML 2006, Representable Cylindric Algebras, Strong Amalgamation Property