3 ms·
Why do you think the same thing doesn't apply to theories? Since you mention topos theory, the double-negation topology is actually a basic construction in topo
by cwzwarich 7y ago
Why do you think the same thing doesn't apply to theories? Since you mention topos theory, the double-negation topology is actually a basic construction in topos theory, used to construct a dense Boolean subtopos of a given topos.
- mikorym 6y agoYou can always generate substructures with closure properties. The subobject structure comes from all the subobjects—so it is the default logic of the topos. Of course you can do the same thing here as you mentioned since it is a Heyting algebra at the least. My point is something else: I don't know of a way to have a intuitionistic exterior logic and a classical internal logic.