Theories and Ordinals in Proof Theory

Synthese 148 (3):719-743 (2006)
  Copy   BIBTEX

Abstract

How do ordinals measure the strength and computational power of formal theories? This paper is concerned with the connection between ordinal representation systems and theories established in ordinal analyses. It focusses on results which explain the nature of this connection in terms of semantical and computational notions from model theory, set theory, and generalized recursion theory

Categories

Keywords

Reprint years

DOI

10.1007/s11229-004-6297-0

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

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: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.
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.
The non-constructive μ operator, fixed point theories with ordinals, and the bar rule.Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):305-324.
Fixed points in Peano arithmetic with ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.
How to develop Proof‐Theoretic Ordinal Functions on the basis of admissible ordinals.Michael Rathjen - 1993 - Mathematical Logic Quarterly 39 (1):47-54.
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.
Reverse mathematics and well-ordering principles: A pilot study.Bahareh Afshari & Michael Rathjen - 2009 - Annals of Pure and Applied Logic 160 (3):231-237.
Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM. [REVIEW]Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (1):35-55.
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.
Some theories with positive induction of ordinal strength ϕω.Gerhard Jäger & Thomas Strahm - 1996 - Journal of Symbolic Logic 61 (3):818-842.
The strength of extensionality I—weak weak set theories with infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
Ordinal diagrams for Π3-reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
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.

Analytics

Added to PP
2009-01-28

Downloads
64 (#243,546)

6 months
4 (#698,851)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Michael Rathjen
University of Leeds

Citations of this work

Predicativity and Feferman.Laura Crosilla - 2017 - In Gerhard Jäger & Wilfried Sieg (eds.), Feferman on Foundations: Logic, Mathematics, Philosophy. Cham: Springer. pp. 423-447.
Slow consistency.Sy-David Friedman, Michael Rathjen & Andreas Weiermann - 2013 - Annals of Pure and Applied Logic 164 (3):382-393.
Set theory: Constructive and intuitionistic ZF.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.

Add more citations

References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.

View all 20 references / Add more references