Research Article

Interpolation and amalgamation in modal cylindric algebras

Published in: Quaestiones Mathematicae
Volume 43 , issue 9 , 2020 , pages: 1209–1238

DOI: 10.2989/16073606.2019.1605628

Author(s): Tarek Sayed Ahmed , Egypt

Keywords: 03B50 , 03B52 , 03G15 , 03B50 , 03B52 , 03G15

Abstract

Let α be an ordinal and L be a unimodal logic (like S4 or S5). A modal cylindric algebra of dimension α, an LCA _α, is a cylindric algebra of dimension α, expanded with α-many L modalities. For a frame (U, R) of L, each k < α, one defines a diamond box operator on . This defines the semantics of the L modalities in set algebras, with the rest of the operations defined like in cylindric set algebras of dimension α. We study interpolation properties for the corresponding predicate logic having α-many variables. Our results are valid for any reflexive L whose frames contain the universal frames (U, U × U ). In particular, they hold for K5CA _α, S4CA _α (which is an algebraizable extension of topological predicate logic with semantics induced by Alexandrov topologies).

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