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TUCS Seminar: There is no Model Theory for Formal Arithmetic

On Tuesday, January 17th, 2017, Docent Patrick Sibelius (Åbo Akademi University) will given a TUCS Seminar talk entitled "There is no Model Theory for Formal Arithmetic".
The seminar will be held in room 115A (Agora), starting 13.00 (entrance via room 116).
The host of the seminar is Prof. Ion Petre (Åbo Akademi University).

Abstract: The notorious tension between Gödel's second incompleteness theorem of formal arithmetic and Gentzen's consistency theorem of formal arithmetic is approached in a strictly formal manner. A modification of the semantic tableau method is being used herein. Using it it is proved that formal Peano arithmetic is formally inconsistent with idea that Peano arithmetic is true in the standard First-order model of arithmetic. Commonly accepted ways to evade such a result are commented on. By considering a strictly fiormal and finitistic version (interpretation) of the proof of Cantor's Theorem about the cardinality of the set of real numbers an argument is presented that entails that P is not equal NP.

The seminar is based on a TUCS Technical report "Problem Solving by being strict on Finitism".

Short bio: Patrick Sibelius is lecturer in CS at Åbo Akademi, docent at Åbo Akademi, PhD at Stanford University and Uppsala University. He has made research mainly on the relationships between formal logic and empirical sciences, modern physics, in particular. Sibelius has been active in cultural debate.