Universal algebra in higher types
type: Item
instance of: scholarly article
title: Universal algebra in higher types
zbMATH Open document ID: 0777.08008
DOI: 10.1016/0304-3975(92)90310-C
author: Karl Meinke
published in: Theoretical Computer Science
publication date: 1993-01-17T00:00:00Z
review text: In this highly readable paper, the author outlines applications of the elementary theory of higher-type universal algebra to the theory of computation. The underlying motif is the application of abstract ideas of many-sorted universal algebra (in the sense of, e.g., \textit{P. M. Cohn's} book on universal algebra [Universal algebra (1965; Zbl 0141.010)] to theoretical computer science. The important role of recursivity in the computational aspects of the algebraic techniques is not clear to this reviewer; i.e., one is neither developing a recursive category theory nor a recursive universal algebra. A useful completeness theorem is proved. Further, there are interesting discussions of extensions of G. Birkhoff's Variety Theorem and A. I. Mal'tsev's Quasivariety Theorem.
Mathematics Subject Classification ID: 08A70
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 03B15
zbMATH DE Number: 96048
zbMATH Keywords: higher-order logics
zbMATH Keywords: ultraproducts
zbMATH Keywords: concurrent processing
zbMATH Keywords: Horn classes
zbMATH Keywords: applications of the elementary theory of higher-type universal algebra to the theory of computation
zbMATH Keywords: many-sorted universal algebra
zbMATH Keywords: recursivity
reviewed by: Albert A. Mullin
describes a project that uses: Miranda
MaRDI profile type: Publication
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full work available at URL: 0304-3975(92)90310-c
OpenAlex ID: W1966640938
description: scientific article; zbMATH DE number 96048