synthetic domain theory

Synthetic domain theory, as its name suggests, is a synthetic axiomatization of domain theory, typically in toposes. The slogan for synthetic domain theory is that “domains are sets”, or more precisely, “domains are certain intuitionistic sets” in that one works in an intuitionistic set theory with certain anti-classical axioms and defines a notion of domain internally. These synthetic domains act like the analytic notions in that domains support arbitrary fixed points and solutions to...