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Erschienen in:
2000 | OriginalPaper | Buchkapitel
Iteration Algebras Are Not Finitely Axiomatizable
verfasst von : Stephen L. Bloom, Zoltán Ésik
Erschienen in: LATIN 2000: Theoretical Informatics
Verlag: Springer Berlin Heidelberg
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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 axiomatization 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”.