Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.
A non-standard analysis of a cultural icon: The case of Paul Halmos.Logica Universalis10(2016), no
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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.