On representation of cylindric algebras
by
Miklos Ferenczi
Budapest University of Technology, Department of Algebra

The natural algebraizations of first order logic e.g. locally finite cylindric (or locally finite quasi polyadic) algebras do not form a variety. Omitting the locally finiteness we get a variety but representability by set algebras goes wrong in a sense. We present an algebraization F which is a variety and there is a nice representation by set algebras too (denote Crs* this class of set algebras). The axioms of F origin from the extended system (by the merry-go-round identities) of cylindrical axioms if the commutativity of cylindrifications (C4) is replaced by that of substitutions. We can prove that, similarly to the classical case, there is a class K of algebras such that an algebra A is representable (it is in ICrs*) if and only if A is a neat subreduct of an algebra in K with dimension large enough.

Date received: July 7, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caoc-17.