×

On the logic of continuous algebras. (English) Zbl 0667.08004

The paper is concerned with the logic of inequalities appropriate for continuous algebras. Deduction rules are given for separately Z- continuous algebras and also for Z-continuous algebras. The main content of the paper is the investigation of the completeness theorems for these deduction rules, i.e., the theorems stating that an inequality is deducible from a collection E of inequlities iff it holds in each model of E. The completeness of these rules is proved for finitary algebras. For infinitary algebras, the completeness theorem if proved for Z- continuous algebras under the condition that each directed set is a Z- set. It is also shown that it does not hold in general, by giving counterexamples.
Reviewer: H.Yutani

MSC:

08B05 Equational logic, Mal’tsev conditions
PDFBibTeX XMLCite
Full Text: DOI