The Hahn-Banach extension theorem is at once main pillar of functional analysis and—due
to its notorious nature as consequence of the axiom of choice—prime example of a pure …

As a form of the Axiom of Choice about relatively simple structures (posets), Hausdorff's
Maximal Chain Principle appears to be little amenable to computational interpretation. This …

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a
projective object in the category of sets. In constructive ZF (CZF) the existence of enough …

This thesis presents an investigation into large sets and large set axioms in the context of the
constructive set theory CZF. We determine the structure of large sets by classifying their von …

If a continuous function on a complete metric space has approximate roots and in a uniform
manner at most one root, then it actually has a root. We validate this heuristic principle in …

The axiom of choice is equivalent to the shrinking principle: every indexed cover of a set has
a refinement with the same index set which is a partition. A simple and direct proof of this …

In the present note, we study a generalization of Dedekind cuts in the context of constructive
Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's …

Abstract 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 …

This article considers two alternative and formally weaker forms of Fullness, one of the
axioms of constructive Zermelo–Fraenkel set theory. The relation to other axioms is …

If a continuous function on a complete metric space has approximate roots and in a uniform
manner at most one root, then it actually has a root. We validate this heuristic principle in …