Author:
BIRYUKOV PETER,MISHKIN VALERY
Abstract
A criterion of isomorphism for symmetry groups of set ideals is provided in terms of ideal quotients and
cardinal invariants. Furthermore, set ideals with complete symmetry group are characterized. They form
a wide class, comprising, for example, all uniform dense ideals and the ideals of ‘thin’ sets in separable
metric spaces. If the symmetry group of a set ideal is not complete, then its outer automorphism group
is shown to be cyclic of order 2.