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Nk , and return “true” if we find in one of them numbers m1 , . . , mn such that ψ(n1 , . . , nk , m1 , . . , mn ) is true in it. From the fact that ψ is (σN , FN )-absolute, it easily follows that this procedure halts with the correct answer in case R(n1 , . . , nk ), and never halt otherwise. The last theorem shows a very close connection between (semi)-computability and (upward) absoluteness. However, further research is needed in order to understand the full connection between these notions.

3, 1989 (1989) 13. : Relational catamorphisms. V. (1991) 287–318 14. : Demonic operators and monotype factors. Mathematical Structures in Computer Science 3(4) (1993) 417–433 15. : Algebra of Programming. Prentice-Hall International (1996) 16. : Polynomial relators. : Proceedings of the 2nd Conference on Algebraic Methodology and Software Technology, AMAST’91, Springer-Verlag, Workshops in Computing (1992) 303–326 17. : Types, abstraction and parametric polymorphism. : IFIP ’83. Elsevier Science Publishers (1983) 513–523 18.

In particular, we give an elementary equational specification of the 0-totalised rational function field Q0 (X) with its degree operator as an auxiliary function. 1 Introduction Between 1979 and 1995 in cooperation with J V Tucker we wrote a series of papers that classified the computable, semicomputable and cosemicomputable data types using algebraic specifications (see Bergstra and Tucker [2, 3, 4, 5]). , by Marongiu and Tulipani [22] and by Khoussainov [20, 21]). Recently, we have returned to the foundations of the subject in [7, 8], tackling the specification of basic data types such as the rational numbers, and we continue here.

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