d-simple sets, small sets, and degree classes

On Pre-θ-Open Sets and Two Classes of Functions

Semi-θ-Open Sets and New Classes of Maps

Operations, sets and classes

Operational set theory, in the form described below, is an enterprise which consolidates classical set theory with some central concepts of Feferman’s explicit mathematics. It provides for a careful distinction between operations and set-theoretic functions and as such reconciles set theory with needs arising in constructive environments and even in those enhanced by computer science. In the fo...

Conceptualism: sets and classes

We outline an extension of Martin’s view of a conceptual realism, to a Cantorian realm of absolute infinities. We then formulate a strong reflection principle within this framework to obtain extra-constructible large cardinals.

Taxonomic classes of sets

A taxonomic class is a family of nonempty sets such that either every two of its sets are disjoint or one is contained in the other. A complete taxonomic class is one in which every set is the union of the minimal sets contained in it. A connected taxonomic class has exactly one maximal set. The main results are exact and asymptotic formulas for the number of these classes and maximal taxonomic...