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On the NoCounterexample Interpretation
 J. SYMBOLIC LOGIC
, 1997
"... In [15],[16] Kreisel introduced the nocounterexample 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 firstorder Peano arithmetic PA one can find ordinal recursive f ..."
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In [15],[16] Kreisel introduced the nocounterexample 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 firstorder 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
Admissible Proof Theory And Beyond
 Logic, Methodology, and the Philosophy of Science IX, Elsevier
, 1994
"... This article will survey the state of the art nowadays, in particular recent advance in proof theory beyond admissible proof theory, giving some prospects of success of obtaining an ordinal analysis of \Pi ..."
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Cited by 5 (2 self)
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This article will survey the state of the art nowadays, in particular recent advance in proof theory beyond admissible proof theory, giving some prospects of success of obtaining an ordinal analysis of \Pi
KripkePlatek Set Theory And The AntiFoundation Axiom
"... . The paper investigates the strength of the AntiFoundation Axiom, AFA, on the basis of KripkePlatek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength. MSC:03F15,03F35 Keywords: Antifoundation axiom, KripkePlate set theory ..."
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. The paper investigates the strength of the AntiFoundation Axiom, AFA, on the basis of KripkePlatek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength. MSC:03F15,03F35 Keywords: Antifoundation axiom, KripkePlate set theory, subsystems of second order arithmeic 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in differing fields such as mathematical logic, computer science, artificial intelligence, linguistics, cognitive science, and philosophy. Logicians first explored set theories whose universe contains what are called nonwellfounded sets, or hypersets (cf. [6], [2]). But the area was considered rather exotic until these theories were put to use in developing rigorous accounts of circular notions in computer science (cf. [4]). Instead of the Foundation Axiom these set theories adopt the socalled AntiFoundation Axiom, AFA, which gives rise to a rich universe of ...
This document in subdirectoryRS/97/42/
, 1997
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS