Abstract
This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: \( \mathsf {ZFCA}_{\sigma }\) (Zermelo–Fraenkel set theory (with Choice) with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.
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