Finitary Polyadic Algebras from Cylindric Algebras

Abstract

It is known that every α-dimensional quasi polyadic equality algebra (QPEAα) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties \((CA^{+}_\alpha, \alpha \geq 4)\). The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally equivalent to QPEA. It is shown, among others, that from every algebra in \(CA^{+}_\alpha\) a β-dimensional algebra can be obtained in QPEAβ where \(\beta < \alpha (\beta \geq 4)\) , moreover the algebra obtained is representable in a sense.