An Ordinal-Free Proof of the Cut-elimination Theorem for an Impredicative Subsystem of Π1-Analysis with ω-rule

Applications of Cut-Free Infinitary Derivations to Generalized Recursion Theory

Cut elimination is the main tool in proof theoretical research. The emphasis there, however, is on the cut–elimination procedure, i.e., the dynamical aspect of cut–elimination. In this paper we want to show that also the statical aspect, i.e., the mere existence of cut–free derivations, has consequences which may be viewed to belong to Descriptive Set Theory or Generalized Recursion Theory. We ...

Admissible Proof Theory And

1 Prologue Ordinals made their entrance in proof theory through Gentzen's second consistency proof for Peano Arithmetic by transsnite induction up to " 0 , the latter being applied only to decidable predicates (cf. Gentzen 1938]). Gentzen's constructive use of ordinals as a method of analyzing formal theories has come to be a paradigm for much of proof theory from then on, particularly as exemp...

Cut elimination theorem for the second order arithmetic with the π1 1-comprehension axiom and the ω-rule

Admissible Proof Theory and Beyond

Ordinals made their entrance in proof theory through Gentzen’s second consistency proof for Peano Arithmetic by transfinite induction up to ε0, the latter being applied only to decidable predicates (cf. Gentzen [1938]). Gentzen’s constructive use of ordinals as a method of analyzing formal theories has come to be a paradigm for much of proof theory from then on, particularly as exemplified in t...

Draft Completeness and Cut-elimination in the Intuitionistic Theory of Types

In this paper we give a semantic proof of cut-elimination for ICTT. ICTT is an intuitionistic formulation of Church’s theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the λprolog programming language. Our approach, extending techniques of Takahashi, Andrews and tableaux machinery of Fitting, Smullyan, Nerode and Shore, is to prove a comple...