(en) 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.
Mawanda, M.-M. (1988). Well-ordering and Choice in Toposes. Journal of Pure and Applied Algebra, 50(2), 171-184. https://doi.org/10.1016/0022-4049(88)90113-2 (Original work published 1988)