While propositional modal logic is a standard tool, first-order modal logic is not. Indeed, it is not generally understood that conventional first-order syntax is insufficiently ex...
In this paper we describe the promoted tyft tyxt rule format for de ning higher-order languages. The rule format is a generalization of Groote and Vaandrager's tyft tyxt form...
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
In the early 1920s, Pavel Urysohn proved his famous lemma (sometimes referred to as "first non-trivial result of point set topology"). Among other applications, this lemm...
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Syl...