Abstract
The chapter proves Herbrand theorem by considering a formula Y provable in an open theory T. Reasoning by reductio ad absurdum, the chapter supposes that none of the Herbrand disjunctions H n is provable in T and adjoined to the theory T as new axioms ∼ H n (n = 1, 2,…). The definition of the algebra L* as well as the inductive definition of the function v ϑ use the notion of arbitrary set. The proof of lemma cannot thus be formalized in elementary arithmetic, whereas the original proof of Herbrand and the proof of Hilbert and Bernays can easily be formalized there.
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