Leibnizian infinitesimals can be formalized using ringinals in a conservative extension of ZF set theory without the axiom of choice or ultrafilters.
Of pashas, popes, and indivisibles
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abstract
The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other critics. An issue that has been studied in less detail concerns the theological underpinnings of the contemporary debate over indivisibles, its historical roots, the geopolitical situation at the time, and its relation to the ultimate suppression of Cavalieri's religious order. We analyze sources from the 17th through 21st centuries to investigate such a relation.
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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.