62 citations · 126 across the 28 of their papers we have counts for
5 papers · 1 filter
The Herbrand Topos
Benno van den Berg
We define a new topos, the Herbrand topos, inspired by the modified realizability topos and our earlier work on Herbrand realizability. We also introduce the category of Herbrand a…
Are There Enough Injective Sets?
Peter Aczel, Benno van den Berg, Johan Granstroem +1
The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough…
A functional interpretation for nonstandard arithmetic
Benno van den Berg, Eyvind Briseid, Pavol Safarik
We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Goedel and Shoenfield can be used to rewri…
Non-deterministic inductive definitions
Benno van den Berg
We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call "non-deterministic inductive definitions". We give applications…
No-go theorems for functorial localic spectra of noncommutative rings
Benno van den Berg, Chris Heunen
Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices…