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math.LO2025
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…
math.LO2025
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…