Cylindric polyadic algebras have the superamalgamation

TL;DR

This paper proves that cylindric polyadic algebras possess the superamalgamation property using two different proof techniques, enhancing understanding of their algebraic and logical structure.

Contribution

The paper establishes superamalgamation for cylindric polyadic algebras, providing both a Henkin construction and a duality-theoretic proof, which was previously unknown.

Findings

Cylindric polyadic algebras have superamalgamation property.

Two distinct proofs are provided: Henkin construction and duality theory approach.

The results deepen the algebraic and logical understanding of these structures.

Abstract

We show that cylindric polyadic algebras introduced by Ferenczi has the superamalgmation property. We give two proofs. One is a Henkin construction, and the other is inspired by duality theory in modal logic between finite zig zag products of Kripke frames and their complex algebras.