Department Mathematik



Mathematisches Kolloquium

Am Freitag, 25. Juni 2010, um 16 Uhr c.t. spricht

Prof. Dr. Michael Rathjen
(University of Leeds)

im Hörsaal A027 über das Thema

Konsistenz verlangsamt

Zusammenfassung: It is a striking empirical fact that many ``natural'' theories, i.e. theories which have something like an ``idea'' to them, are comparable with regard to consistency strength. This has actually been proved in many cases for theories whose ideas and motivations have nothing at all to do with one another. For example, in set theory, with a few exceptions, large cardinal axioms have been shown to form a well-ordered hierarchy when ordered with regard to consistency strength. A large chunk of the talk will be devoted to surveying logical and mathematical results concerned with the notion of consistency. In last part of the talk I intend to address a simple question. Let PA be the usual first order number theory whose axiomatization goes back to Dedekind and Peano, and let Con(PA) be the statement that PA is consistent. Is there a sense in which PA + Con(PA) is the least "natural" theory whose consistency strength is greater than that of PA? Any new results reported in this talk are joint work with Sy Friedman and Andreas Weiermann. The question whether to give the talk in German or in English I intend to play by ear (i.e. the kind of audience?).
Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.
Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.