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A termination proof for epsilon substitution using partial derivations

✍ Scribed by G. Mints

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
351 KB
Volume
303
Category
Article
ISSN
0304-3975

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✦ Synopsis

Epsilon substitution method introduced by Hilbert is a successive approximation process providing numerical realizations from proofs of existential formulas. Most convergence (termination) proofs for it use assignments of decreasing ordinals to stages of the process and work only for predicative systems. We describe a new ordinal assignment for the case of ÿrst-order arithmetic admitting extension to impredicative systems. It is based on an interpretation of individual epsilon substitutions forming the substitution process as incomplete ÿnite proofs, each encoding a complete but inÿnite proof.

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