Weakly higher order cylindric algebras and finite axiomatizationof the representables

摘要

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