Proof theory for theories of ordinals II: Π3-reflection

Annals of Pure and Applied Logic 129 (1-3):39-92 (2004)
  Copy   BIBTEX

Abstract

This paper deals with a proof theory for a theory T3 of Π3-reflecting ordinals using the system O of ordinal diagrams in Arai 1375). This is a sequel to the previous one 1) in which a theory for recursively Mahlo ordinals is analyzed proof-theoretically

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2004.01.001

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Proof theory for theories of ordinals II:< i> Π_< sub> 3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
Ordinal diagrams for Π3-reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
About the proof-theoretic ordinals of weak fixed point theories.Gerhard Jäger & Barbara Primo - 1992 - Journal of Symbolic Logic 57 (3):1108-1119.
Review: Wilfried Buchholz, Notation Systems for Infinitary Derivations ; Wilfried Buchholz, Explaining Gentzen's Consistency Proof within Infinitary Proof Theory ; Sergei Tupailo, Finitary Reductions for Local Predicativity, I: Recursively Regular Ordinals. [REVIEW]Toshiyasu Arai - 2002 - Bulletin of Symbolic Logic 8 (3):437-439.
Ordinal diagrams for recursively Mahlo universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.
The [mathematical formula] quantification operator in explicit mathematics with universes and iterated fixed point theories with ordinals.Markus Marzetta & Thomas Strahm - 1997 - Archive for Mathematical Logic 36 (6):391-413.
Consistency proof via pointwise induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.
Some theories with positive induction of ordinal strength ϕω.Gerhard Jäger & Thomas Strahm - 1996 - Journal of Symbolic Logic 61 (3):818-842.
The proof-theoretic analysis of transfinitely iterated fixed point theories.Gerhard JÄger, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
Some Theories with Positive Induction of Ordinal Strength $varphiomega 0$.Gerhard Jager & Thomas Strahm - 1996 - Journal of Symbolic Logic 61 (3):818-842.
Review: Samuel R. Buss, Handbook of Proof Theory: An Introduction to Proof Theory. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):464-465.

Analytics

Added to PP
2014-01-16

Downloads
24 (#642,030)

6 months
8 (#347,798)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Proof theory of weak compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
Epsilon Substitution Method for [image] -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.

View all 11 citations / Add more citations

References found in this work

Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Pure proof theory aims, methods and results.Wolfram Pohlers - 1996 - Bulletin of Symbolic Logic 2 (2):159-188.
Ordinal diagrams for Π3-reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
x1. Aims.Wolfram Pohlers - 1996 - Bulletin of Symbolic Logic 2 (2):159-188.

View all 6 references / Add more references