Pfender, Michael2021-12-172021-12-172012-12-212197-8085https://depositonce.tu-berlin.de/handle/11303/15730http://dx.doi.org/10.14279/depositonce-14503Gödel 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.en510 MathematikGödel Theoremscategorical recursiondecidabilityconsistency provabilityResearch Paper