Simple proof of Zermelo's theorem
  Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper is to propose a simple proof of this theorem. Please inform us if you ever encountered such a proof. 
V. V. Filippov, E. Yu. Mychka
math.GN