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The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory

  • Irving H. Anellis

Abstract

Warren Goldfarb (1971, p. 17) wrote that “Herbrand’s work had an immediate impact on the Hilbert school,” and quotes Paul Bernays (Hilbert and Bernays, 1934, 1939, 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.

Keywords

Quantification Theory Natural Deduction Proof Theory Axiomatic Method Natural Deduction System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Irving H. Anellis
    • 1
  1. 1.Modern Logic PublishingAmesUSA

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