Department Mathematik



Mathematisches Kolloquium

Am Freitag, 08. Februar 2013, um 16 Uhr c.t. spricht

Prof. Dr. Stanley S. Wainer
(University of Leeds)

im Hörsaal A027 über das Thema

Goodstein Sequences, Fast Growing Functions and Arithmetical Independence Results

Zusammenfassung: Formalized arithmetical theories, that supply logical foundations for large parts of mathematics, have ordinals associated with them, measuring their consistency strength. Important examples are Peano Arithmetic and (much stronger) Pi-1-1 Comprehension. Furthermore, up to the given ordinal, the so-called Fast Growing Hierarchy of number-theoretic functions serves to measure the theory's computational power. In addition, these functions turn out to be closely connected with certain known theorems of combinatorial mathematics, which then become independence results (true but not provable) for the given theories. In this way, certain mathematical results serve to calibrate the logical strengths of the theories concerned. This talk will give a brief survey of the role of the Fast Growing Hierarchy in this area, beginning with Goodstein Sequences and the independence from PA (first proved by Kirby and Paris in 1982) of Goodstein's result (1944) that they always terminate.

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.