# Talk by Ali Enayat (LTCS)

Short Title:

Talk by Ali Enayat

Event Date(s):

Thursday, 23. November 2017 - 13:30

**Venue**

Room A097, ExWi, Sidlerstrasse 5, 3012 Bern

**Speaker**

Prof. Dr. Ali Enayat (University of Gothenburg)

**Title**

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

**Abstract**

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:

- 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.
- 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''.

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