4 papers · 1 filter
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…