We introduce a general notion of convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections in the lattice of opens.Expand

Abstract Overlap algebras are complete lattices enriched with an extra primitive relation, called “overlap”. The new notion of overlap relation satisfies a set of axioms intended to capture, in a… Expand

We analyze the concepts of finite set and finite subset from the perspective of a minimalist foundational theory which is “minimalist” in the sense that it can be seen as the common core of some of the most used foundations.Expand

We generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.Expand

With Raoult’s Open Induction in place of Zorn’s Lemma, we do a perhaps more perspicuous proof of Lindenbaum’s Lemma for not necessarily countable languages of first-order predicate logic. We… Expand

A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation.Expand