Iteration Algebras Are Not Finitely Axiomatizable. Extended Abstract
Stephen L. Bloom, Zoltán Ésik · 2000
Stephen L. Bloom and Zoltan Esik # 1 Stevens Institute of Technology Department of Computer Science Hoboken, NJ 07030 [email protected] 2 A. Jozsef University Department of Computer Science Szeged, Hungary [email protected] Abstract. Algebras whose underlying set is a complete partial order and whose termoperations are continuous may be equipped with a least fixed point operation x.t. The set of all equations involving the -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".