Abstract
It is known that every α-dimensional quasi polyadic equality algebra (QPEA α ) 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 QPEA β where \(\beta < \alpha (\beta \geq 4)\) , moreover the algebra obtained is representable in a sense.
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Supported by the OTKA grants T0351192, T43242.
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Ferenczi, M. Finitary Polyadic Algebras from Cylindric Algebras. Stud Logica 87, 1–11 (2007). https://doi.org/10.1007/s11225-007-9073-6
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DOI: https://doi.org/10.1007/s11225-007-9073-6