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pro vyhledávání: '"Williams, Kameryn J."'
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 PA [Visser2006], ZF, Z2, and KM [enayat2017]. In this article we exten
Externí odkaz:
http://arxiv.org/abs/2212.04445
Autor:
Barton, Neil, Williams, Kameryn J.
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-theoretic potentialism, before proving some results concerning the relev
Externí odkaz:
http://arxiv.org/abs/2108.01543
Autor:
Williams, Kameryn J.
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 smaller inner models. I show: (A) it is possible that the $\omega$-th inn
Externí odkaz:
http://arxiv.org/abs/2106.07812
We investigate how set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for information about a model of set theory $\langle M,\in^M\rangle$, we explain senses in which one may compute $M$-generic
Externí odkaz:
http://arxiv.org/abs/2007.00418
We introduce the $\Sigma_1$-definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, (i) the sequence is $\Sigma_1$-definable and provably
Externí odkaz:
http://arxiv.org/abs/1909.09100
Autor:
Reitz, Jonas, Williams, Kameryn J
We present a class forcing notion $\mathbb M(\eta)$, uniformly definable for ordinals $\eta$, which forces the ground model to be the $\eta$-th inner mantle of the extension, in which the sequence of inner mantles has length at least $\eta$. This ans
Externí odkaz:
http://arxiv.org/abs/1810.08702
Autor:
Habič, Miha E., Hamkins, Joel David, Klausner, Lukas Daniel, Verner, Jonathan, Williams, Kameryn J.
Publikováno v:
Arch. Math. Logic 58 (7-8), 2019, 965-997
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 showed that any finite poset embeds into the generic multiverse while
Externí odkaz:
http://arxiv.org/abs/1808.01509
Autor:
Williams, Kameryn J
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 the structure of models of second-order set theories. The main
Externí odkaz:
http://arxiv.org/abs/1804.09526
Autor:
Williams, Kameryn J
In this article I investigate the phenomenon of minimum models of second-order set theories, focusing on Kelley--Morse set theory $\mathsf{KM}$, G\"odel--Bernays set theory $\mathsf{GB}$, and $\mathsf{GB}$ augmented with the principle of Elementary T
Externí odkaz:
http://arxiv.org/abs/1709.03955
Autor:
WILLIAMS, KAMERYN J.
Publikováno v:
The Journal of Symbolic Logic, 2019 Jun 01. 84(2), 589-620.
Externí odkaz:
https://www.jstor.org/stable/26788464