/sci/ - Science & Math

>>9048417
>but the independence of (not-)AC from ZF means you can have both ZFC and ZFnC
I know, but don't I need to explicitly add an axiom which states that AC is false?
>Therefore, you can add this P as your axiom
I want to prove the negation of AC from the other axioms. The theory doesn't have to be ZF.

>constructivistic logic
It doesn't refute LEM or AC. I need a theory which allows me to prove the negation of choice, I don't care about LEM that much.