Iterative algebras, defined by the property that every guarded system of recursive equations has a unique solution, are proved to have a much stronger property: every system of recursive equations has a unique strict solution. Those systems that have a unique solution in every iterative algebra are characterized.
Keywords: iterative algebra, guarded equation, strict solution, extensive category
2000 MSC: 68Q65, 18A15
Theory and Applications of Categories,
Vol. 19, 2007,
No. 5, pp 61-92.