First Order Theories for Nonmonotone Inductive Definitions: Recursively Inaccessible and Mahlo

Journal of Symbolic Logic 66 (3):1073-1089 (2001)
  Copy   BIBTEX

Abstract

In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms a la Richter with recursively inaccessible and Mahlo closure ordinals is given.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

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

Through your library

Similar books and articles

The Recursively Mahlo Property in Second Order Arithmetic.Michael Rathjen - 1996 - Mathematical Logic Quarterly 42 (1):59-66.
A note on theories for quasi-inductive definitions.Riccardo Bruni - 2009 - Review of Symbolic Logic 2 (4):684-699.
Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Ordinal diagrams for recursively Mahlo universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.
Induction–recursion and initial algebras.Peter Dybjer & Anton Setzer - 2003 - Annals of Pure and Applied Logic 124 (1-3):1-47.
Ordinal analysis of non-monotone-definable inductive definitions.Wolfram Pohlers - 2008 - Annals of Pure and Applied Logic 156 (1):160-169.
Ordinal analysis by transformations.Henry Towsner - 2009 - Annals of Pure and Applied Logic 157 (2-3):269-280.
Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.

Analytics

Added to PP
2009-01-28

Downloads
233 (#79,351)

6 months
1 (#1,040,386)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
Proof theory of reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
A well-ordering proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
Proof theory and ordinal analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.

View all 9 references / Add more references