Author(s) :
Michael Pfender
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 14-2016
MSC 2000
- 03F03 Proof theory, general
-
18A05 Definitions, generalizations
Abstract :
The consistency formula for gödelian Arithmetics T can be stated as free-variable predicate in terms of the categorical theory PR of primitive recursive functions/maps/predicates. Free-variable p.r. predicates are decidable by gödelian theory T, key result, built on recursive evaluation of p.r. map codes and soundness of that evaluation into theories T : internal, arithmetised p. r. map code equality is evaluated into map equality of T. In particular the free-variable p.r. consistency predicate of T is decided by T. Therefore, by Gödel's second in- completeness theorem, gödelian quantified Arithmetics T turn out to be self-inconsistent.
Keywords :
primitive recursion, categorical free-variables Arithmetic, code evaluation, Stimmigkeit, soundness, decidability of PR predicates, Goedel theorems, self-inconsistency of quantified arithmetical theories