Operations, sets and classes
Jäger, Gerhard Max
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 following we consider, primarily from a proof-theoretic perspective, the theory OST and some of its most important extensions and determine their consistency strengths by exhibiting equivalent systems in the realm of traditional theories of sets and classes.