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.