In Gitman et al. (2020), my coauthors and I mounted a set-theoretic analogue of reverse mathematics in the context of second-order set theory, working over Gödel-Bernays set theory (but without the power-set axiom) as a base theory, a considerably stronger axiomatic framework. A rich hierarchy of natural axiomatizations and theorem equivalents has emerged. For example, the class forcing theorem (the assertion that every class forcing notion admits a forcing relation) is equivalent to the principle of elementary transfinite recursion, to the existence of Ord-iterated truth predicates, to the
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