9 citations · 9 across the 5 of their papers we have counts for
5 papers
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…
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu +21
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most…
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…
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…
A choiceless box game paradox
Elliot Glazer
We identify a choiceless variation of the box game paradox, in which players predict unknown real numbers with near-perfect accuracy despite lacking any useful information. We also…