The Independence of Stone's Theorem from ZF | Department of Mathematics

The Independence of Stone's Theorem from ZF

Event Information
Event Location: 
GAB 461
Event Date: 
Wednesday, April 23, 2014 - 3:30pm

M.E. Rudin's proof of Stone's theorem begins with well-ordering an open cover. Good, Tree, and Watson, being set theorists and thus naturally suspiscious of such a move, investigated whether the axiom of choice was necessary for Stone's theorem to be true. In 1996 they showed that in a certain choiceless universe there is a metric space which is not paracompact: a counter-example to Stone's theorem. We will be loosely following their presentation and will prove the same result.