Michael Pfender: Self-Inconsistency of set theory

Sep 28, 2017 | 03:00 PM



The consistency formula for set theory T e. g. Zermelo-Fraenkel set theory ZF; 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 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, the free-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.

Time & Location

Sep 28, 2017 | 03:00 PM

FU Berlin | Arnimallee 6 | Raum 108/109