Moser, Georg, and Richard Zach. 2006. “The Epsilon Calculus and Herbrand Complexity.” Studia Logica 82 (1): 133–55. https://doi.org/10.1007/s11225-006-6610-7.
Hilbert’s \(\varepsilon\)-calculus is based on an extension of the language of predicate logic by a term-forming operator \(\varepsilon x\). Two fundamental results about the \(\varepsilon\)-calculus, the first and second epsilon theorem, play a role 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.
Review: Mathematical Reviews 2205042 (2006k:03127) (Mitsuru Yasuhara)