Timeline for Number of paths through infinite trees with given "growth rates"

11 events

when toggle format	what		by	license	comment
May 26, 2021 at 15:31	vote	accept	usul
Nov 7, 2014 at 11:31	comment	added	Joel David Hamkins		Yes, I agree. But there is an analogous result, however, for at-most $d$-branching trees $T\subset d^{<\omega}$, using $d^n$ in place of $2^n$.
Nov 7, 2014 at 7:52	comment	added	Douglas Zare		There is an assumption in your first theorem that is not present in the question. Your assumption that there are at most $2$ children of each node makes the question more interesting. Without this, it might be that only the first node has multiple children, in which case the number of branches is countable.
Nov 7, 2014 at 2:41	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 68 characters in body
Nov 7, 2014 at 2:33	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 228 characters in body
Nov 7, 2014 at 2:15	comment	added	Joel David Hamkins		There is an unsettled middle ground for growth rates between $o(2^n)$ and $\Omega(2^n)$, and it isn't clear to me what is going on there.
Nov 7, 2014 at 2:05	history	edited	Joel David Hamkins	CC BY-SA 3.0	deleted 1 character in body
Nov 7, 2014 at 1:55	history	edited	Joel David Hamkins	CC BY-SA 3.0	More precise positive and negative results
Nov 7, 2014 at 0:55	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 1784 characters in body
Nov 7, 2014 at 0:50	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 1784 characters in body
Nov 6, 2014 at 22:51	history	answered	Joel David Hamkins	CC BY-SA 3.0