Inhalt des Dokuments
Preprint 38-2012
Arithmetical Foundations
Author(s) :
Michael Pfender
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 38-2012
MSC 2000
- 03G30 Categorical logic, topoi
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03B30 Foundations of classical theories
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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