Is the consistency of classical third-order arithmetic (PA$_3$) provable in the logic of a topos with natural numbers?
(My guess would be yes, but I haven't seen this anywhere.)
Question. My question in broad terms: what are the uses of entropy in geometric analysis, particularly in variational contexts to study sequences of functionals such as the two results described below? [See at the bottom for a more precise version of the question.]
Several branches of mathematics...
In case somebody is curious what is the purpose of this room, I have tried to give some explanation when creating the room.
Of course, basically anything what can be found here can also be found through SEDE, some queries are suggested here: What would be good place to list unresolved bounties? But perhaps searching in chat is easier for some users. Moreover, here you also get a brief preview of the question.
$\newcommand{\Grp}{\mathrm{Grp}}$Consider the category of groups $\Grp$, and within it we have the solvable groups $S$. Then any group $G$ determines the functor from solvable groups: $$h_G:=\text{hom}_{\Grp}(\_,G):S^{\mathrm{op}}\rightarrow \text{Set}$$
Does this functor determine the group $G$?...
Listing bounties and HNQs
Listing bounties and HNQs