| Résume | Motivated by several recent advances, we will provide a research history of the main set-theoretic problems arising in the study of strong homology. We will presume no knowledge, in our audience, of the latter. The aforementioned advances close out a second major phase of research in this area, leaving just a few conspicuous last "first questions," and our aim is to provide some context for engaging them. This research centers on multidimensional combinatorial phenomena generalizing the classical theme of \emph{nontrivial coherent families indexed by $^\omega\omega$}; its progress has involved an intriguing mix of classical (forcing axioms, iterations of large cardinal length) and novel (higher-dimensional $\Delta$-systems, simplicial combinatorics) set-theoretic techniques. |
