Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Pfender, Michael
PY - 2017
TI - Self-Inconsistency of set theory
DO - 10.14279/depositonce-14662
UR - http://dx.doi.org/10.14279/depositonce-14662
PB - Technische Universität Berlin
LA - en
AB - 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. In particular, thefree-variable p. r. consistency predicate of T is decidable by T. Therefore, by Gödel’s second incompleteness theorem, set theories T turn out to be self-inconsistent.
KW - free variables
KW - Skolem logic
KW - iteration
KW - primitive recursion
KW - gödelisation
KW - map code evaluation
KW - objectivity
KW - arithmetised equality
KW - soundness
KW - predicates
KW - decidability
KW - Gödel theorems
KW - inconsistency provability
ER -