4 papers · 1 filter
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…
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…
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…
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…