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# The Epsilon Calculus and Herbrand Complexity

Georg Moser and Richard Zach
Studia Logica: An International Journal for Symbolic Logic
Vol. 82, No. 1, Cut-Elimination in Classical and Nonclassical Logic (Feb., 2006), pp. 133-155
Stable URL: http://www.jstor.org/stable/20016771
Page Count: 23
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## Abstract

Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon _{x}$. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.

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