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math.LO2022★ 1 cited
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…
math.LO2022★ 2 cited
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…