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math.LO2026
Characterising projective and weakly projective Boolean algebras by coherent Freese--Nation separations
Tomasz Kania, Andrzej Kucharski, Sławomir Turek
We isolate a coherent finite-separation strengthening of the Freese--Nation property and use it to characterise projective and weakly projective Boolean algebras. A Boolean algebra…
math.GN2026
Homogeneity of profinite graphs
Wiesław Kubiś, Andrzej Kucharski, Sławomir Turek
Profinite graphs are inverse limits of sequences of nonempty finite graphs. There exists a ``generic'' graph $\Pe$ in this category, although its edge relation is rather poor: only…