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Hilbert’s Program Then and Now
, 2005
"... Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and els ..."
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Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of Göttingen and elsewhere in the 1920s
The epsilon calculus and Herbrand Complexity
 STUDIA LOGICA
, 2006
"... Hilbert’s εcalculus is based on an extension of the language of predicate logic by a termforming operator εx. Two fundamental results about the εcalculus, the first and second epsilon theorem, play a rôle similar to that which the cutelimination theorem plays in sequent calculus. In particular ..."
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Hilbert’s εcalculus is based on an extension of the language of predicate logic by a termforming operator εx. Two fundamental results about the εcalculus, the first and second epsilon theorem, play a rôle similar to that which the cutelimination 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.
G.Moser R.Zach The Epsilon Calculus and
, 2005
"... Abstract. Hilbert’s εcalculus is based on an extension of the language of predicate logic by a termforming operator εx. Two fundamental results about the εcalculus, the first and second epsilon theorem, play a rôle similar to that which the cutelimination theorem plays in sequent calculus. In pa ..."
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Abstract. Hilbert’s εcalculus is based on an extension of the language of predicate logic by a termforming operator εx. Two fundamental results about the εcalculus, the first and second epsilon theorem, play a rôle similar to that which the cutelimination 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. Keywords: Hilbert’s εcalculus, epsilon theorems, Herbrand’s theorem, proof complexity 1.