??so what _about_ relationship between two (??...) aspects of ... ??whether boolean algebra of "boolean-valued model" (or something ...) is co-/complete ... ??...

1 ??something about quantifiers ... extending [assignment of truth values to generators] to quantified statements as well ... ??or something ....

2 ??something about ... ???pretopos vs topos, and stone space vs boolean locale, and so forth ... ???....