Notes on some second-order systems of iterated inductive definitions and Π11-comprehensions and relevant subsystems of set theory.

Kentaro Fujimoto

doi:10.1016/j.apal.2014.11.001

^{Notes on some second-order systems of iterated inductive definitions and Π₁¹-comprehensions and relevant subsystems of set theory.}

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Abstract

Pohlers's ordinal analysis in his monograph [12] contains some flaws and thereby ends up with incorrect proof-theoretic ordinals of several systems. The present paper determines their correct proof-theoretic ordinals and also supplements [12] with the ordinal analysis of some other relevant impredicative systems.

Original language	English
Pages (from-to)	409-463
Number of pages	55
Journal	Annals of Pure and Applied Logic
Volume	166
Issue number	4
Early online date	16 Dec 2014
DOIs	https://doi.org/10.1016/j.apal.2014.11.001
Publication status	Published - 1 Apr 2015

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Dr Kentaro Fujimoto
- Kentaro.Fujimotobristol.acuk
- School of Mathematics - Lecturer
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Cite this

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title = "Notes on some second-order systems of iterated inductive definitions and Π11-comprehensions and relevant subsystems of set theory. ",

abstract = "Pohlers's ordinal analysis in his monograph [12] contains some flaws and thereby ends up with incorrect proof-theoretic ordinals of several systems. The present paper determines their correct proof-theoretic ordinals and also supplements [12] with the ordinal analysis of some other relevant impredicative systems.",

author = "Kentaro Fujimoto",

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N2 - Pohlers's ordinal analysis in his monograph [12] contains some flaws and thereby ends up with incorrect proof-theoretic ordinals of several systems. The present paper determines their correct proof-theoretic ordinals and also supplements [12] with the ordinal analysis of some other relevant impredicative systems.

AB - Pohlers's ordinal analysis in his monograph [12] contains some flaws and thereby ends up with incorrect proof-theoretic ordinals of several systems. The present paper determines their correct proof-theoretic ordinals and also supplements [12] with the ordinal analysis of some other relevant impredicative systems.

U2 - 10.1016/j.apal.2014.11.001

DO - 10.1016/j.apal.2014.11.001

M3 - Article (Academic Journal)

VL - 166

SP - 409

EP - 463

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 4

ER -

Notes on some second-order systems of iterated inductive definitions and Π11-comprehensions and relevant subsystems of set theory.

Abstract

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Dr Kentaro Fujimoto

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^{Notes on some second-order systems of iterated inductive definitions and Π₁¹-comprehensions and relevant subsystems of set theory.}