Zermelo's Well-Ordering Theorem in Type Theory
by
Danko Ilik
BibTeX
@MISC{Ilik_zermelo'swell-ordering,
author = {Danko Ilik},
title = {Zermelo's Well-Ordering Theorem in Type Theory},
year = {}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Abstract. Taking a `set ' to be a type together with an equivalence relation and adding an extensional choice axiom to the logical framework (a restricted version of constructive type theory) it is shown that any `set' can be well-ordered. Zermelo's rst proof from 1904 is followed, with a simpli cation to avoid using comparability of well-orderings. The proof has been formalised in the system AgdaLight. 1
