# Arithmetical Foundations: Recursion. Evaluation. Consistency

## Inst. Mathematik

Gödel Theorems revisited. Categorical free-variables theory of Primitive Recursion and of mu-recursion. Definition of evaluation of PR codes as Complexity Controlled Iteration, introduction of a theory piR of non-infinite descent of such iterations. (Termination conditioned) Soundness of evaluation. Decidability of PR free-variable predicates. Decidability of Consistency formulae for piR and set theory as special cases. omega-inconsistency of set theory and derivability of consistency formula for Descent theory piR as consequences.