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
    =====================

    Set Theories with a Universal Set
    ----------------------------------
    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
    a widespread misconception that Russell's paradox proves that the
    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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