Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols (Classic Logic Papers, Pt. 4)

You probably all know the result that Peano Arithmetic is not finitely axiomatizable (a result due to Ryll-Nardzewski), and a similar result for ZFC (due to Richard Montague, I believe). The standard axiom system for PA is not finite since the axiom scheme of induction stands for infinitely many sentences. Ryll-Nardzewski showed that there is … Continue reading Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols (Classic Logic Papers, Pt. 4)