Non-finite axiomatisability of reducts of algebras of relations

Ian Hodkinson and Szabolcs Mikulás

30 pages.  Submitted, September 1998.
 

Abstract:

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based.   We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras.


Nonfinite axiomatisability of reducts of relation and cylindric algebras

Ian Hodkinson and Szabolcs Mikulás

ILLC prepublication series, ML-1997-04, Sep. 1997, c. 16 pages.

In this paper, we show that certain subreducts of the class of representable relation algebras are not finitely axiomatizable. We do the same for sequential and cylindric algebras.

This is an earlier version of Nonfinite axiomatisabiliy of reducts of relation algebras above.