Archive for Mathematical Logic 39 (5):353-391 (2000)

Abstract
In this paper we introduce a recursive notation system $O(\mu)$ of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each $\alpha<\Omega$ in $O(\mu)$ KPM proves that the initial segment of $O(\mu)$ determined by $\alpha$ is a well ordering. Proof theoretic study for such theories will be reported in [9]
Keywords Legacy
Categories (categorize this paper)
DOI 10.1007/s001530050153
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,795
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Epsilon Substitution Method for [Π0 1, Π0 1]-FIX.T. Arai - 2005 - Archive for Mathematical Logic 44 (8):1009-1043.
A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.

View all 6 citations / Add more citations

Similar books and articles

Ordinal Diagrams for Π3-Reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
Proof-Theoretic Analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
The Recursively Mahlo Property in Second Order Arithmetic.Michael Rathjen - 1996 - Mathematical Logic Quarterly 42 (1):59-66.
Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
On the Plurality of Gods.Eric Steinhart - 2013 - Religious Studies 49 (3):289-312.
Consistency Proof Via Pointwise Induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.
Ein Wohlordnungsbeweis Für Das OrdinalzahlensystemT(J).K. Schütte - 1988 - Archive for Mathematical Logic 27 (1):5-20.

Analytics

Added to PP index
2013-11-23

Total views
19 ( #550,525 of 2,438,771 )

Recent downloads (6 months)
1 ( #436,491 of 2,438,771 )

How can I increase my downloads?

Downloads

My notes