A General Theory of Class Symmetric Systems

Abstract: We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present sufficient conditions for the preservation of the axioms of Gödel-Bernays set theory (without the axiom of choice), and for the forcing theorem to hold for class-sized symmetric systems.