Nordic Online Logic Seminar: next talk on April 25 by Michael Rathjen

[Graham Leigh]

The Nordic Online Logic Seminar (NOL Seminar) is organised monthly over Zoom, with expository talks on topics of interest for the broader logic community. The seminar is open for professional or aspiring logicians and logic aficionados worldwide.

See the announcement for the next talk below. If you wish to receive the Zoom ID and password for it, as well as further announcements, please subscribe here: https://listserv.gu.se/sympa/subscribe/nordiclogic .

Val Goranko and Graham Leigh
NOL seminar organisers
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Nordic Online Logic Seminar

Next talk: Monday, April 25, 16.00-17.30 CEST (UTC+2), on Zoom (details are provided to the seminar subscribers)

Title: Completeness: Turing, Schütte, Feferman (and Löb)

Speaker: Michael Rathjen, Professor in Pure Mathematics, University of Leeds

Abstract:
Progressions of theories along paths through Kleene’s Omega adding the consistency of the previous theory at every successor step, can deduce every true Π^1_0-statement. This was shown by Turing in his 1938 thesis who called these progressions “ordinal logics”. In 1962 Feferman proved the amazing theorem that progressions based on the “uniform reflection principle” can deduce every true arithmetic statement. In contrast to Turing’s, Feferman’s proof is very complicated, involving several cunning applications of self-reference via the recursion theorem. Using Schütte’s method of search trees (or decomposition trees) for omega-logic and reflexive induction, however, one can give a rather transparent proof.
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