Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits

Abstract

Abstract. We establish some basic properties of quotients of projective Fraïssé limits and exhibit some classes of compact metric spaces that are the quotient of a projective Fraïssé limit of a projective Fraïssé family in a finite language. We prove the result for the arcs directly, and by applying some closure properties we obtain all hypercubes and graphs as well.

A Categorical Characterization of Accessible Domain

“…This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation (contributed to [1]). In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up.…”