Talk by Ali Enayat (LTCS)

Short Title: 
Talk by Ali Enayat
Event Date(s): 
Thursday, 23. November 2017 - 13:30

Room A097, ExWi, Sidlerstrasse 5, 3012 Bern

Prof. Dr. Ali Enayat (University of Gothenburg)

On the theory NBG + "the class of ordinals is weakly compact".

The talk will discuss various results related to the strengthening of NBG (von Neumann-Gödel-Bernays class theory) with an axiom stating that the class of ordinals is weakly compact. The discussion will include the following results:

  1. NGB + ``the class of ordinals is weakly compact'' is conservative over the extension of ZFC obtained by adding the scheme whose instances are statements of the form ``there is an n-reflective n-Mahlo cardinal'', where n ranges over natural numbers in the meta-theory.
  2. No canonical model of NBG, i.e., one obtained by adjoining the definable classes to a model of ZF, satisfies ``the class of ordinals is weakly compact''.