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Weakly higher order cylindric algebras and finite axiomatization of the representables

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Abstract

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Réaltanoda u., 1053, Budapest, Hungary

    I. Németi

  2. Mathematical Institute, Technical University, Budapest, H-1111 Egry József utca 1, Budapest, Hungary

    A. Simon

Authors
  1. I. Németi
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  2. A. Simon
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Correspondence to I. Németi.

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Supported by the Hungarian National Foundation for Scientific Research grant T73601.

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Németi, I., Simon, A. Weakly higher order cylindric algebras and finite axiomatization of the representables. Stud Logica 91, 53–62 (2009). https://doi.org/10.1007/s11225-009-9162-9

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  • DOI: https://doi.org/10.1007/s11225-009-9162-9

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