# July 2: T. Forstner, Set Theories with a Universal Set

From: Helmut Veith (kgs-owner@dbai.tuwien.ac.at)
Date: Mon Jun 24 2002 - 12:28:20 MEST

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Lecture Announcement
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Set Theories with a Universal Set
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Thomas Forstner, Cambridge

ABSTRACT: Russell's paradox shows that naive set theory is inconsistent,
and that we must exercise care in selecting axioms for set theory. It is
collection of all sets is not itself a set. There are demonstrably
consistent set theories with a universal set, but sadly the best known -
and least understood, Quine's NF, is not yet one of them. The consistency
problem for NF remains open. NF is derived from Simple Type theory (see
Carnap's *Abriss der Logistik* (1929), and most approaches to the question
of the consistency problem arise from these roots of NF. I shall be
explaining Specker's important reduction of the consistency problem for NF
(See: Specker, E. P. Dualit\"at. {\sl Dialectica} {\bf 12} pp. 451$-$465.)
NFU, a closely related system with Urelemente, is known to be consistent,
and I shall be discussing the contrast between these two situations.

TIME: Tuesday, July 2, 17:15

PLACE: Seminaraum des Institutes für Algebra und Computermathematik
Technische Universität Wien, Freihaus, Wiedner Hauptstrasse 8-10 grüne Zone,
5.Stock Seminarraum 118

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