This paper develops a formal approach to evaluating freedom in interactive settings based on the literatures on preference for flexibility and measurement of diversity. The approach posits that freedom has an instrumental component–grounded in preferences– and an intrinsic component. The philosophical justification and implications of the approach are considered. In particular, we discuss the n...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.