On the No-Counterexample Interpretation (1997)
by
Ulrich Kohlenbach
| Venue: | J. SYMBOLIC LOGIC |
| Citations: | 12 - 4 self |
BibTeX
@ARTICLE{Kohlenbach97onthe,
author = {Ulrich Kohlenbach},
title = {On the No-Counterexample Interpretation},
journal = {J. SYMBOLIC LOGIC},
year = {1997},
volume = {64},
pages = {1491--1511}
}
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Abstract
In [15],[16] Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated "-substitution method (due to W. Ackermann), that for every theorem A (A prenex) of first-order Peano arithmetic PA one can find ordinal recursive functionals \Phi A of order type ! " 0 which realize the Herbrand normal form A of A. Subsequently more
