论文信息 - Proof-theoretic analysis of KPM

Proof-theoretic analysis of KPM

AbstractKPM is a subsystem of set theory designed to formalize a recursively Mahlo universe of sets. In this paper we show that a certain ordinal notation system is sufficient to measure the proof-theoretic strength ofKPM. This involves a detour through an infinitary calculus RS(M), for which we prove several cutelimination theorems. Full cut-elimination is available for derivations of $$\Sigma (L_{\omega _1^c } )$$ sentences, whereω1c denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical point of view.

Michael Rathjen | M. Rathjen

[1] Gerhard Jäger,et al. ϱ-inaccessible ordinals, collapsing functions and a recursive notation system , 1984, Arch. Math. Log..

[2] Michael Rathjen,et al. Ordinal notations based on a weakly Mahlo cardinal , 1990, Arch. Math. Log..

[3] Wolfram Pohlers. Ordinal notations based on a hierarchy of inaccessible cardinals , 1987, Ann. Pure Appl. Log..

[4] C. Smorynski. The Incompleteness Theorems , 1977 .

[5] Stephen G. Simpson,et al. Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume , 1985, Arch. Math. Log..

[6] Wayne Richter. Recursively Mahlo Ordinals and Inductive Definitions , 1971 .

[7] Wilfried Buchholz,et al. Proof Theory of Impredicative Subsystems of Analysis , 1988 .

[8] Leo Harrington. The Superjump and the First Recursively Mahlo Ordinal , 1974 .

[9] Wolfram Pohlers. Proof Theory: An Introduction , 1990 .

[10] Gerhard Max Jäger,et al. Theories for admissible sets : a unifying approach to proof theory , 1986 .

[11] Wolfram Pohlers,et al. Proof theory and ordinal analysis , 1991, Arch. Math. Log..

[12] Wilfried Buchholz,et al. A new system of proof-theoretic ordinal functions , 1986, Ann. Pure Appl. Log..

[13] Jon Barwise,et al. Admissible sets and structures , 1975 .