So: First Order Logic, ZFC, Second-Order Logic and Simple Type Theory. But : Church (Lambda Calculus), Curry (Combinatory Logic), and Brouwer (Intuitionist) while overlapping with Set Theory, each go in slightly different directions that doesn’t necessarily adhere to the same foundations as Set Theory. That said, I still don’t think you can have them without a strong knowledge of Set Theory, for even though they work off different assumptions, historically they’re linked and draw from it.

So:
First Order Logic,
ZFC,
Second-Order Logic and
Simple Type Theory.
But :
Church (Lambda Calculus), Curry (Combinatory Logic), and Brouwer (Intuitionist)
while overlapping with Set Theory, each go in slightly different directions that doesn’t necessarily adhere to the same foundations as Set Theory.
That said, I still don’t think you can have them without a strong knowledge of Set Theory, for even though they work off different assumptions, historically they’re linked and draw from it.

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