Iteration algebras are not finitely axiomatizable

Stephen L. Bloom, Zoltán Ésik

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

Algebras whose underlying set is a complete partial order and whose term-operations are continuous may be equipped with a least fixed point operation μx.t. The set of all equations involving the μ-operation which hold in all continuous algebras determines the variety of iteration algebras. A simple argument is given here reducing the ax-iomatization of iteration algebras to that of Wilke algebras. It is shown that Wilke algebras do not have a finite axiomatization. This fact implies that iteration algebras do not have a finite axiomatization, even by "hyperidentities".

Original languageEnglish
Title of host publicationLATIN 2000
Subtitle of host publicationTheoretical Informatics - 4th Latin American Symposium, Proceedings
Pages367-376
Number of pages10
DOIs
Publication statusPublished - Dec 1 2000
Event4th Latin American Symposium on Theoretical Informatics, LATIN 2000 - Punta del Este, Uruguay
Duration: Apr 10 2000Apr 14 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1776 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th Latin American Symposium on Theoretical Informatics, LATIN 2000
CountryUruguay
CityPunta del Este
Period4/10/004/14/00

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bloom, S. L., & Ésik, Z. (2000). Iteration algebras are not finitely axiomatizable. In LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings (pp. 367-376). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1776 LNCS). https://doi.org/10.1007/10719839_36