For this question, mathematics is defined as the set of theorems generated from Zermelo-Fraenkel axioms, with the addition of axiom of choice.
The answers that I seek are:
Is it possible to provide a set of axioms that underlie the whole of theoretical computer science?
Can these axioms of theoretical computer science be derived from Zermelo-Fraenkel axioms?
Furthermore, Zermelo-Fraenkel axioms must not be derivable from these axioms otherwise the two set of axioms would be equivalent to each other?
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