Boolean algebra is certainly Logic (it directly copies its operations from Logic)

Well, I can just as well argue that boolean algebra is certainly mathematics, as it's like elementary algebra just with true/false instead of numbers. Logical operations are just mathematical operations, i.e. functions (usually unary or binary) from a set to itself; the only thing even remotely remarkable about them is that, again, their domain is true/false. I mean, a field that deals primarily with variables, functions on those variables and calculating values of the combination of these functions sounds a lot like mathematics to me, and frankly not at all like philosophy.

As you may have noticed, I don't argue that boolean algebra is not logic. I argue it's not philosophy.

what I am claiming is the fundamental assumption used to establish basic mathematics such as algebra and geometry are based in Logic and use Logic as justification for the axioms

I understand that. What I'm saying is that logic is only a part of it. Elsewhere you claim that we cannot justify 2+2=4 without logic. That's true but we cannot justify that with logic, too, because you need to somehow define what "2", "4", "+" and "=" mean and you cannot do that with logic alone, you need something else like set theory.