Abstract
Polyadic algebras were introduced and intensively studied by Halmos, after having studied cylindric algebras in Tarski’s seminar in Berkeley; we refer to Section 5.4 of [Hen-Mon-Tar,85], see also [Hal,62]. This class of algebras can be regarded as an alternative approach to algebraize first order logic. After a thorough reformulation of Henkin, Monk, and Tarski, polyadic algebras also can be regarded as certain generalizations of cylindric algebras. On one hand, polyadic algebras have nice representation properties, on the other, their languages are rather large (in the ω-dimensional case the cardinality of their set of operations is continuum), which makes their equational theory recursively undecidable for trivial reasons. This is undesirable from metalogical point of view, hence, during the last decades, certain countable (even finite) reducts of polyadic algebras have also been intensively studied. The goal of this research direction is to find a countable reduct of polyadic algebras which has nice representation properties, and, at the same time, their equational theory is recursively enumerable.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 János Bolyai Mathematical Society and Springer-Verlag
About this chapter
Cite this chapter
Sági, G. (2013). Polyadic Algebras. In: Andréka, H., Ferenczi, M., Németi, I. (eds) Cylindric-like Algebras and Algebraic Logic. Bolyai Society Mathematical Studies, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35025-2_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-35025-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35024-5
Online ISBN: 978-3-642-35025-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)