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A SIMPLIFIED PROOF OF THE EPSILON THEOREMS

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  10 July 2023

STEFAN HETZL Open the ORCID record for STEFAN HETZL [Opens in a new window]
STEFAN HETZL*
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY TU WIEN, WIEDNER HAUPTSTRASSE 8-10 1040 VIENNA, AUSTRIA URL: https://www.dmg.tuwien.ac.at/hetzl/
*
E-mail: stefan.hetzl@tuwien.ac.at
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Abstract

We formulate Hilbert’s epsilon calculus in the context of expansion proofs. This leads to a simplified proof of the epsilon theorems by disposing of the need for prenexification, Skolemisation, and their respective inverse transformations. We observe that the natural notion of cut in the epsilon calculus is associative.

Keywords

proof theoryepsilon calculusexpansion proofsHerbrand’s theorem

MSC classification

Primary: 03F05: Cut-elimination and normal-form theorems 03F07: Structure of proofs
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 16
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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