19 citations · 36 across the 9 of their papers we have counts for
9 papers · 1 filter
Non-tightness in class theory and second-order arithmetic
Alfredo Roque Freire, Kameryn J. Williams
A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including…
Varieties of class-theoretic potentialism
Neil Barton, Kameryn J. Williams
We explain and explore class-theoretic potentialism -- the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-th…
The -th inner mantle
Kameryn J. Williams
This article investigates pathological behavior at the first limit stage in the sequence of inner mantles, obtained by iterating the definition of the mantle to get smaller and sma…
The Sigma_1-definable universal finite sequence
Joel David Hamkins, Kameryn J. Williams
We introduce the -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extensio…
Inner mantles and iterated HOD
Jonas Reitz, Kameryn J Williams
We present a class forcing notion , uniformly definable for ordinals , which forces the ground model to be the -th inner mantle of the extension, in which the s…
Set-Theoretic Blockchains
Miha E. Habič, Joel David Hamkins, Lukas Daniel Klausner +2
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…
The Structure of Models of Second-order Set Theories
Kameryn J Williams
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 st…
Minimum models of second-order set theories
Kameryn J Williams
In this article I investigate the phenomenon of minimum models of second-order set theories, focusing on Kelley--Morse set theory , Gödel--Bernays set theory $\mathsf{…
The exact strength of the class forcing theorem
Victoria Gitman, Joel David Hamkins, Peter Holy +2
The class forcing theorem, which asserts that every class forcing notion admits a forcing relation , that is, a relation satisfying the forcing re…