??so what about "boolean locale" corresponding to ... ???"cocomplete boolean algebra"?? ... ??or something ???... ??what about such coming from a top space, for example an alexandroff space ?? ....

??something about "coherence" here... ??something about lots of examples that we have where double negation topos of a coherent topos seems to be coherent ... ??but then there should be lots of examples where it's not, right?? ...??what are some nice prototypical examples of this ??? ...

??regular opens in a top space (??or something??) as forming what ... ??... regularization as adjoint ... ??? or something ??? ....

??"boolean frame" ... ???...

?regularly closed subsets of one-point compactification of natural numbers ...

??something about... ??what's going on with forcing ... ???... ??boolean frame?? ... ??poset of forcing conditions ...???coherence ?? ...

??so what _about_ ... ??point of talking about general idea of "forcing semantics" ??? ...

??so what _about_ something about ... "freely distributively adjoining colimits up to a certain nice cardinal, then completely freely adjoining them up to another certani nice cardinal" ... ??and so forth ...