Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.
Extrait d’une Lettre de M. Leibnitz ` a M. Varignon, contenant l’explication de ce qu’on a raport´ e de luy dans les Memoires de Trevoux des mois de Novembre & Decembre derniers
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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.