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math.LO2026
More on the Boolean Prime Ideal Theorem
Jacob Kowalczyk, Jindrich Zapletal
We prove the consistency of Zermelo--Fraenkel set theory with the Axiom of Dependent Choices, no Vitali sets and a large fragment of the Boolean Prime Ideal Theorem.
math.LO2025
Cardinalities of Ultraproducts of Finite Sets in ZF + DC
Jacob Kowalczyk
It is consistent with ZF + DC that there exists an ultrafilter on such that two infinite ultraproducts of finite sets, and , have the same c…