>>11101924>>11102115>>11102253No it doesn't. Set theory, like group theory, are just common examples for the kind of theories logic enables you to write down.
There is a notion of collection in logic, namely the universe of discourse, but it's not a "set". You don't speak of membership (or intersections, etc.) there.
Logic stands on its own and just requires the capacity of rewriting
https://en.m.wikipedia.org/wiki/Abstract_rewriting_system>>11102019No, you can write down category theory as a first order theory and define subobjects via what amounts to characteristic functions in pullbacks. This is just commuting diagrams
