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 are quite unambiguously-defined and attested mathematical definitions, the first is a highly context-dependent notion (that anyone can apply to their favorite context, mathematical or not). Perhaps more precisely put: each of the latter three form a category, or perhaps even more precisely put, each of the latter three are structures in the usual sense of model theory, while the first is not known to either be a category or a class of structures, in any reasonable way. More coming soon.