Refinement is equivalent to Fullness

In the article [4], a new constructive set theoretic principle called Refinement was introduced and analysed. While it seemed to be significantly weaker than its alternative, the more established axiom of Fullness (a constructive version of the Powerset axiom from classical set theory), it was shown to suffice to imply many of the mathematically important consequences. In this article, we will define for each set A a set of truth values which...