A central area of current philosophical debate in the foundations of mathematics concerns
whether or not there is a single, maximal, universe of set theory. Universists maintain that …

In this article we introduce and study hyperclass-forcing (where the conditions of the forcing
notion are themselves classes) in the context of an extension of Morse-Kelley class theory …

MODERN CLASS FORCING 1. Introduction Set theorists started forcing with class partial
orders to modify global properties of the Page 1 MODERN CLASS FORCING CAROLIN …

The principle of open determinacy for class games—two-player games of perfect information
with plays of length ω, where the moves are chosen from a possibly proper class, such as …

After reviewing various natural bi-interpretations in urelement set theory, including second-
order set theories with urelements, we explore the strength of second-order reflection in …

We show that Kelley-Morse set theory does not prove the class Fodor principle, the assertion
that every regressive class function $ F: S\to\text {Ord} $ defined on a stationary class $ S …

Jensen used♦ to construct a forcing notion J of perfect trees which has the ccc and adds a
unique generic real. Given an inaccessible κ, we generalize Jensen's construction, using♦ …

We show that the Boolean algebras approach to class forcing can be carried out in the
theory Kelley-Morse plus the Choice Scheme (KM+ CC) using hyperclass Boolean …

Given a countable model of set theory, we study the structure of its generic multiverse, the
collection of its forcing extensions and ground models, ordered by inclusion. Mostowski …

This dissertation is a contribution to the project of second-order set theory, which has seen a
revival in recent years. The approach is to understand second-order set theory by studying …