Infinitesimal analysis without the Axiom of Choice

摘要: Abstract It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom Choice than traditional elementary analysis. The claim based on observation hyperreals entail existence nonprincipal ultrafilters over N , a strong version Choice, while real numbers can be constructed in ZF. axiomatic approach to nonstandard methods refutes this objection. We formulate theory SPOT st-∈-language which suffices carry out infinitesimal arguments, and prove conservative extension Thus Calculus are just as effective those Calculus. conclusion extends large parts ordinary mathematics beyond. also develop stronger system SCOT, ZF + ADC suitable for handling such features an Lebesgue measure. Proofs conservativity results combine extend forcing developed by Enayat Spector.