Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.
Historical infinitesimalists and modern historiogra- phy of infinitesimals.Antiquitates Mathematicae16(2022), 189–257
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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.