Iteration algebras are not finitely axiomatizable

Stephen L. Bloom, Z. 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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages367-376
Number of pages10
Volume1776 LNCS
DOIs
Publication statusPublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Algebra
Iteration
Axiomatization
Partial Order
Fixed point
Imply
Term

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bloom, S. L., & Ésik, Z. (2000). Iteration algebras are not finitely axiomatizable. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1776 LNCS, 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

Iteration algebras are not finitely axiomatizable. / Bloom, Stephen L.; Ésik, Z.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1776 LNCS 2000. p. 367-376 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1776 LNCS).

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

Bloom, SL & Ésik, Z 2000, Iteration algebras are not finitely axiomatizable. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1776 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1776 LNCS, pp. 367-376, 4th Latin American Symposium on Theoretical Informatics, LATIN 2000, Punta del Este, Uruguay, 4/10/00. https://doi.org/10.1007/10719839_36
Bloom SL, Ésik Z. Iteration algebras are not finitely axiomatizable. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1776 LNCS. 2000. p. 367-376. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/10719839_36
Bloom, Stephen L. ; Ésik, Z. / Iteration algebras are not finitely axiomatizable. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1776 LNCS 2000. pp. 367-376 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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