The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory
Irving H. Anellis · Birkhäuser Boston eBooks · 2008
Warren Goldfarb (1971, p. 17) wrote that “Herbrand’s work had an immediate impact on the Hilbert school,” and quotes Paul Bernays (, vol. 1, “Foreword”) to the effect that “the appearance of the works of Herbrand and Gödel have altered proof theory.” We are concerned here to explore the role which Herbrand’s work had in developing the discipline of proof theory. More specifically, we are interested in formulating a theory about the impact which questions raised by Herbrand, about the meaning of satisfiability in Hilbert’s axiomatic method, had on the proliferation of quantification theories presented as alternatives to Hilbert’s system.