3 problems

A singular strong limit cardinal is a singular cardinal $\gk$ such that $2^{\gk'}$ is less than $\gk$ for every cardinal $\gk'<\gk$. The Singular Cardinal Hypothesis. If $\gk$ is a…

Let $\mu$ range over singular cardinals, and write $\operatorname{Pr}_1(\mu^+,\mu^+,\mu^+,\operatorname{cf}(\mu))$ for the corresponding strong coloring principle. Failure conjectu…

Let $obreakbreak obreaklambda$ be a singular cardinal with $obreakbreak obreaklambda<mu$, and let $D$ be a $(lambda^+,mu)$-regular ultrafilter. **Singular-cardinal regular-ultraf…