Herbrand's Fundamental Theorem in the Eyes of Jean van Heijenoort

Claus-Peter Wirth

In: Logica Universalis, Vol. 6, Pages 485-520, Springer Publishing House, 2012.


Using Heijenoort’s unpublished generalized rules of quantification, we discuss the proof of Herbrand’s Fundamental Theorem in the form of Heijenoort’s correction of Herbrand’s “False Lemma” and present a didactic example. Although we are mainly concerned with the inner structure of Herbrand’s Fundamental Theorem and the questions of its quality and its depth, we also discuss the outer questions of its historical context and why Bernays called it “the central theorem of predicate logic” and considered the form of its expression to be “concise and felicitous”.

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence