Bibliographic Details
| Title: |
A termination proof for epsilon substitution using partial derivations |
| Authors: |
Mints, G.1 mints@turing.stanford.edu |
| Source: |
Theoretical Computer Science. Jun2003, Vol. 303 Issue 1, p187. 27p. |
| Subjects: |
Stochastic convergence, Approximation theory |
| Abstract: |
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 first-order arithmetic admitting extension to impredicative systems. It is based on an interpretation of individual epsilon substitutions forming the substitution process as incomplete finite proofs, each encoding a complete but infinite proof. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
