It is known that basic part of recursion theory, such as recursion theory, smn-theorem, recursion theorem and normal form theorem can be formalized in HA [2].

The aim of this talk is to do recursion theory itself more in constructive mathematics. One of the problem is the treatment of complements of sets of natural numbers over intuitionistic logic. In this talk, we adopt the notion of complemented sets by [1] and try to develop degree theory.

Bibliography

1. E. Bishop and D. Bridges,{\bfseries\itshape Constructive Analysis},Springer-Verlag, 1980.
2. A.Troelstra and D. van Dalen,{\bfseries\itshape Constructivism in Mathematics Volumes I},Studies in Logic and the Foundations of Mathematics,Elsevier, 1988.