Implicit expressibility in two-valued logic and cryptoisomorphisms of two-element algebras
type: Item
instance of: scholarly article
title: Implicit expressibility in two-valued logic and cryptoisomorphisms of two-element algebras
zbMATH Open document ID: 0896.06013
author: O. M. Kasim-Zade
published in: Doklady Mathematics
publication date: 1998-05-23T00:00:00Z
review text: The author presents a summary of his results (11 theorems) on the problem of implicit expressibility in two-valued logic, according to \textit{A. V. Kuznetsov} [Logical inference (Logicheskij vyvod), Proc. All-Union Symp. Theory of Logical Inference, Moscow March 1974, 5-33 (1979; Zbl 0605.03001)]. He establishes the equivalence of implicit expressibilty, implicit reducibility, and parametric reducibility and investigates the corresponding notions of implicit closedness and completeness. In conclusion, a classification of algebras on a two-element set is given, up to crypto-isomorphism in the sense of G. Birkhoff. Proofs are not included.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 06E30
Mathematics Subject Classification ID: 03G20
Mathematics Subject Classification ID: 08A62
zbMATH DE Number: 1122763
zbMATH Keywords: classification of two-element algebras
zbMATH Keywords: two-valued logic
zbMATH Keywords: implicit expressibilty
zbMATH Keywords: implicit reducibility
zbMATH Keywords: parametric reducibility
zbMATH Keywords: crypto-isomorphism
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1122763