direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Inhalt des Dokuments

Preprint 08-2017

Self-Inconsistency of set theory

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

Author(s) : Michael Pfender

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 08-2017

MSC 2000

03B30 Foundations of classical theories
18-02 Research exposition

Abstract :
The consistency formula for set theory T e. g. Zermelo-Fraenkel set theory ZF, can be stated in form of a free-variable predicate in terms of the categorical theory PR of primitive recursive functions/maps/predicates. Free-variable p. r. predicates are decidable by T, key result. Decidability is built on recursive evaluation of p. r. map codes and soundness of that evaluation into theory T : internal, arithmetised p. r. map code equality is evaluated into map equality of T. As a free-variable p. r. predicate, the consistency formula of T is decidable by T. Therefore, by Gödel's second incompleteness theorem, set theories T turn out to be self-inconsistent, to derive their own inconsistency formulae.

Keywords : free variables, Skolem logic, iteration, primitive recursion, gödelisation, map code evaluation, objectivity, arithmetised equality, soundness, predicates, decidability, Gödel theorems, inconsistency provability

Zusatzinformationen / Extras


Schnellnavigation zur Seite über Nummerneingabe