Local Constructive Set Theory and Inductive Definitions

Abstract

Local Constructive Set Theory (LCST) is intended to be a local version of constructive set theory (CST). Constructive Set Theory is an open-ended set theoretical setting for constructive mathematics that is not committed to any particular brand of constructive mathematics and, by avoiding any built-in choice principles, is also acceptable in topos mathematics, the mathematics that can be carried out in an arbitrary topos with a natural numbers object.