Algebras whose underlying set is a complete partial order and whose term-operations are continuous may be equipped with a least fixed point operation umx.t. The set of all equations involving the um-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".
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