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math.LO2026
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…
math.LO2024
Global choice is not conservative over local choice for Zermelo set theory
Elliot Glazer
We prove that Global Choice is not conservative over ZC and that ZF Union does not prove existence of for all and . Each proof is by constructing a pathologic…
math.LO2023
A Topological Tennenbaum Theorem
Elliot Glazer
We prove that in Borel models of arithmetic on an uncountable Polish space, neither addition nor multiplication is continuous. This is an analogue of Tennenbaum's Theorem for topol…