Adámek, Jǐri; Mekler, Alan H.; Nelson, Evelyn; Reiterman, Jan On the logic of continuous algebras. (English) Zbl 0667.08004 Notre Dame J. Formal Logic 29, No. 3, 365-380 (1988). 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 Cited in 4 Documents MSC: 08B05 Equational logic, Mal’tsev conditions Keywords:logic of inequalities; continuous algebras; completeness theorems; deduction rules PDFBibTeX XMLCite \textit{J. Adámek} et al., Notre Dame J. Formal Logic 29, No. 3, 365--380 (1988; Zbl 0667.08004) Full Text: DOI