Series: Penn State Logic Seminar Date: Tuesday, March 18, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: Thomas Forster, Cambridge University, Mathematics Title: AC fails in the natural analogues of V and L that model the stratified fragment of ZF Abstract: If G is a group of permutations of V_omega it has countably many different actions on V, since for each n < omega it can move x by permuting the elements bigcup^n x of finite rank and fixing the rest. A set that is fixed by everything in G under the nth action of G is said to be n-symmetric; if it is n-symmetric for all sufficiently large n it is just plain symmetric. The class of hereditarily symmetric sets is a model for the stratified axioms of ZF but contains no wellordering of V_omega! There is also a stratified analogue of L too, but the construction is extremely fragile.