Weakly higher order cylindric algebras and finite axiomatization of the representables

Studia Logica 91 (1):53 - 62 (2009)
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.
Keywords algebraic logic  cylindric algebra  quasi-projective relation algebra  non-well-founded set theory  finitization problem
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