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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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