 Lurking in the background of the state-space conception is the fact that mathematics actually includes set theory and model theory—i.e., mathematical logic. Indeed, according to some interlocutors, “metamathematics is part of mathematics” (Halvorson 2012, 204). Historically, a set-/model-theoretic approach emerged from Tarski’s work and was extensively articulated by Suppes and his associates (van Fraassen 1980, 67). Set theory is a general language for formalizing mathematical structures as collections—i.e., sets—of abstract objects (which can themselves be relations or functions; see Krivine 2013 [1971]). Model theory investigates the relations between, on the one hand, the formal axioms, theorems, and laws of a particular theory and, on the other hand, the mathematical structures—the models—that provide an interpretation of that theory, or put differently, that make the theory’s axioms, theorems, and laws true (Hodges 1997, Chapter 2; Jones 2005). Interestingly, model theory often uses set theory (e.g., Marker 2002); set theory can, in turn, be extended to link axiomatic theories and semantic models via “set-theoretical predicates” (e.g., Suppes 1957, 2002). Finally, there are certain hybrids of these two branches of mathematical logic, including “partial structures” (e.g., da Costa and French 1990, 2003; Bueno 1997; French 2017; French and Ladyman 1999, 2003; Vickers 2009; Bueno, French, and Ladyman 2012). Lorenzano (2013) provides a more complex taxonomy of the intellectual landscape of the Semantic View, including a discussion of Structuralism, a kind of set-/model-theoretic perspective. Structuralism involves theses about “theory-nets,” theory-relative theoretical vs. non-theoretical terms, a diversity of intra- and inter-theoretic laws with different degrees of generality, a typology of inter-theoretic relations, and a rich account of correspondence rules in scientific practice (see Moulines 2002; Pereda 2013; Schmidt 2014; Ladyman 2014). On the whole, the set-/model-theoretic approach of the Semantic View insists on the inseparability of metamathematics and mathematics. In preferring to characterize a theory axiomatically in terms of its intension rather than its extension, it shares the Syntactic View’s aims of reconstructive axiomatization (e.g., Sneed 1979; Stegmüller 1979; Frigg and Votsis 2011; Halvorson 2013, 2019; Lutz 2012, 2014, 2017).