If you're interested in formalizing math, check out Metamath: https://us.metamath.org https://us.metamath.org. By itself Metamath doesn't embed any particular

If you're interested in formalizing math, check out Metamath: https://us.metamath.org https://us.metamath.org. By itself Metamath doesn't embed any particular set of axioms. The most widely used database (axioms and proven theorems) uses classical logic and set theory, but there's also databases for intuitionistic set theory, new foundations, and higher order logic.