Paper detail

On configurations concerning cardinal characteristics at regular cardinals

We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak{s}_θ,\mathfrak{p}_θ,\mathfrak{g}_θ,\mathfrak{r}_θ,\mathfrak{t}_θ$ at uncountable regular cardinals $θ$. Motivated by a theorem of Raghavan-Shelah who proved that $\mathfrak{s}_θ\leq\mathfrak{b}_θ$, we explore in the first part of the paper the consistency of inequalities comparing $\mathfrak{s}_θ$ with $\mathfrak{p}_θ$ and $\mathfrak{g}_θ$. In the second part of the paper we study variations of the extender-based Radin forcing to establish several consistency results concerning $\mathfrak{r}_θ$ from hyper-measurability assumptions, results which were previously known to be consistent only from supercompactness assumptions. In doing so, we answer several questions which appeared in the literature.