Record number :
Title of article :
Bernays–Gödel type theory
Author/Authors :
Carsten Butz، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Pages :
From page :
To page :
Abstract :
We study the type-theoretical analogue of Bernays–Gödel set-theory and its models in categories. We introduce the notion of small structure on a category, and if small structure satisfies certain axioms we can think of the underlying category as a category of classes. Our axioms imply the existence of a co-variant powerset monad on the underlying category of classes, which sends a class to the class of its small subclasses. Simple fixed points of this and related monads are shown to be models of intuitionistic Zermelo–Fraenkel set-theory (IZF).
Journal title :
Journal of Pure and Applied Algebra
Serial Year :
Link To Document :