Osius' set theory

Hello, In his 1974 paper Osius showed that there are enough transitive objects in the initial topos to define a naive set theory. He then goes on the assume his topoi are well-pointedness and produces a characterisation of the category of sets in terms familiar to set theorists. I'm wondering whether anyone has produced an axiomatic set theory from Osius' naive set theory which characterises the initial topos. -- Dr Elwood Wilkins e-mail: elwood@essex.ac.uk Senior Research Officer tel: (+44) (0)1206 872336 Department of Computer Science fax: (+44) (0)1206 872788 University of Essex, Colchester, Essex, UK