LST Numbers for $Q^{\text{e.c.}}$ and $I$ style quantifiers

Abstract

We introduce two schemes of quantifiers analogous to $I$ and $Q^\text{e.c.}$, which tell us about regular cardinals of small Cantor-Bendixson rank. We examine how the L\"owenheim-Skolem-Tarski numbers of these quantifiers interact with one another, and with those of $I$ and $Q^{\text{e.c.}}$. We then find the exact lower bound for each of the LST numbers, assuming the consistency of supercompacts.