??so what _does_ it mean to have a model of a classical first-order theory over the stone space given by 1-point compactification of N? ... ???.... ... somewhat concretely and explicitly ... ??.....

??hmm, so what about something about ... ???stone space (or something...) of subquotients (or something) of a set x ???? .... ???... ???hmm, what _about_ something about "orthogonality of partitions" (or something...) here??? .... ???what about something about "connection information" ?????? .... ????......

??maybe just something about "in-/efficiency" here??

?? ... more generally (...), what about something about ... ??stone space of t-structures on some stuff ... ???or something ... ??...

???hmm, so maybe the subquotients of a set really do form a stone space??? ??or something???... ....solutions of a system of boolean equations ... ??...

???something about ... ??"continuous map from stone space x to stone space of subquotients of s, with union of all the subs equal to s and coarsest mutual refinement of all the quotients equal to actual equality on s" ??? .... ???o something ???....

???but what about some "inefficiency" here ????.....

hmmmm...... ????.....

for example something about if the continuous map is constant ... ???....