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Preprint 38-2012

Arithmetical Foundations

Source file is available as :   Portable Document Format (PDF)

Author(s) : Michael Pfender

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 38-2012

MSC 2000

03G30 Categorical logic, topoi
03B30 Foundations of classical theories
03D75 Abstract and axiomatic computability and recursion theory

Abstract :
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.

Keywords : Gödel Theorems, categorical recursion, decidability, consistency provability

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