It seems underemphasized that the parsimony of ZFC in the way of ‘types’ (having only one sort called sets) has the following practical and notational virtue: you can get by with a single type of the quantifier , and a … Continue reading
For the time being, the installments of the serial ‘Higher Trees Today’ will focus on three kinds of higher trees: Contractible Spaces of Choices (c.s.c.) Diestel–Oum decompositions (d.o.d.) Kalai trees (k.t.) Masbaum-Vaintrob trees (m.v.t.) Of course, while the latter three … Continue reading
Did you know that mathematics will provide you with more-or-less standardized tools to usefully express commonly-occurring ideas? For exaple, the following illustration contains at least three examples of this: (0) the symbol for boundaries of things, the symbol to symbolize … Continue reading
[Disclaimer: this a blog-post consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see https://arxiv.org/abs/1707.09400. Compression ratio here is high. ] This recent preprint of Jørgen Bang-Jensen, Stéphane Bessy, Frédéric Havet, Anders Yeo … Continue reading
[Disclaimer: this a blog-post consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see arXiv:1707.09005 [math.LO]. Compression ratio here is high. ] The recent preprint arXiv:1707.09005 of Michael Lieberman, Jiří Rosický, Sebastien Vasey is … Continue reading
Arguably the simplest non-trivial example of an unlabelled simple undirected graph which is not reconstructible from its vertex-deleted subgraphs is the -regular tree, illustrated in parts by Needfull to say: that you only see five neighbors at each vertex is … Continue reading
Trees of all kinds are of fundamental importance.