Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.
Differentials, higher-order differentials and the derivative in the Leibnizian calculus.Archive for History of Exact Sciences14(1974), 1–90
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A philosophical history of infinitesimals
Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.