Small uncountable cardinals in asymptology

In the talk we shall discuss some cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete, inseparable, large) of finitary or locally finite coarse structures on $\omega$. Besides well-known cardinals $\mathfrak b,\mathfrak d,\mathfrak c$ we shall encounter two new cardinals $\Delta$ and $\Sigma$, defined as the smallest weight of a finitary coarse structure on $\omega$ which contains no discrete subspaces and no asymptotically separated sets, respectively. I can prove that $\max\{\mathfrak b,\mathfrak s,\cov(\mathcal N)\}\le\Delta\le\Sigma\le\non(\mathcal M)$, but I do not know if the cardinals $\Delta,\Sigma,\non(\mathcal M)$ can be distinguished in suitable models of ZFC.

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