### 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 language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 367-376 |

Number of pages | 10 |

Volume | 1776 LNCS |

DOIs | |

Publication status | Published - 2000 |

Event | 4th Latin American Symposium on Theoretical Informatics, LATIN 2000 - Punta del Este, Uruguay Duration: Apr 10 2000 → Apr 14 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1776 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 4th Latin American Symposium on Theoretical Informatics, LATIN 2000 |
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Country | Uruguay |

City | Punta del Este |

Period | 4/10/00 → 4/14/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Iteration algebras are not finitely axiomatizable

AU - Bloom, Stephen L.

AU - Ésik, Z.

PY - 2000

Y1 - 2000

N2 - 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".

AB - 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".

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UR - http://www.scopus.com/inward/citedby.url?scp=84896693003&partnerID=8YFLogxK

U2 - 10.1007/10719839_36

DO - 10.1007/10719839_36

M3 - Conference contribution

SN - 3540673067

SN - 9783540673064

VL - 1776 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 367

EP - 376

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -