2 citations · 3 across the 7 of their papers we have counts for
7 papers
The Iterative Conception Reconsidered
Bokai Yao
We investigate the iterative conception of set in its most general form, allowing urelements without assuming that they form a set. We formulate this conception in two ways, as sta…
Reflection Principles in ZFU
Elliot Glazer, Bokai Yao
We separate the Collection Principle, the Reflection Principle, and the Partial Reflection Principle in ZF with urelements (ZFU), despite their equivalence under the Axiom of Choic…
Abstraction Principles and the Size of Reality
Bokai Yao
The Fregean ontology can be naturally interpreted within set theory with urelements, where objects correspond to sets and urelements, and concepts to classes. Consequently, Fregean…
Plenitudinous Urelements and the Definability of Cardinality
Bokai Yao
The Axiom of Plenitude asserts that every ordinal is equinumerous with a set of urelements, while its stronger form, Plenitude, extends it to all sets. We investigate these two…
Set Theory with Urelements
Bokai Yao
This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement s…
Axiomatization and Forcing in Set Theory with Urelements
Bokai Yao
In the first part of this paper, we consider several natural axioms in urelement set theory, including the Collection Principle, the Reflection Principle, the Dependent Choice sche…
Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal
Joel David Hamkins, Bokai Yao
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…