7 problems

A cardinal $\lambda$ is regular if $\operatorname{cf}(\lambda)=\lambda$, and it is pathological in the sense used in the source when it witnesses the failure of the relevant superc…

The axiom $V=\operatorname{Ultimate}L$ is the assertion that the universe is Ultimate $L$. The Ultrapower Axiom is the assertion that any pair of ultrapower embeddings has an inter…

For a cardinal $\delta$, say that the UA Hypothesis holds at $\delta$ if there is an inner model of the Ultrapower Axiom with the $\delta$-covering and $\delta$-approximation prope…

Let $\kappa$ be a cardinal. A cardinal is measurable if it carries a nonprincipal $\kappa$-complete ultrafilter, and $2^\kappa$ denotes the cardinality of its power set. UA continu…

The Ultrapower Axiom is the assertion that any pair of ultrapower embeddings has an internal ultrapower comparison. An extendible cardinal is a cardinal satisfying the correspondin…

Let $\mathscr B(\lambda)$ denote the class of countably complete incompressible ultrafilters relevant to the Ketonen order. Ketonen-order conjecture. If the Ketonen order is linear…

Assume the Ultrapower Axiom. Let $\delta$ be a regular cardinal and let $\kappa\leq\delta$ be the least $\delta$-strongly compact cardinal. The $<_S$-least uniform countably comple…