Well-ordering and choice in toposes

Abstract

The aim is to show that Zermelo's Theorem fails in general toposes. A weak form of the well-ordering hypothesis (WOT) and two weak forms of choice (AC) and (ACS) are introduced, in order to give sense to Zermelo's Theorem in non-classical toposes. Toposophical models are constructed to show the non validity of Zermelo's Theorem.