metamathematics

Logical-principle and simple formal-system theory {metamathematics} {proof theory, mathematics} can have no infinities, use minimum English, use existence theorems to show how to construct new objects, not use proof by contradiction, not use Zorn's lemma, and not use axiom of choice [Hilbert, 1899] [Kleene, 1952] [Tarski, 1983].

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