Ordinal arithmetic and $\Sigma_{1}$ -elementarity

Archive for Mathematical Logic 38 (7):449-460 (1999)
  Copy   BIBTEX

Abstract

We will introduce a partial ordering $\preceq_1$ on the class of ordinals which will serve as a foundation for an approach to ordinal notations for formal systems of set theory and second-order arithmetic. In this paper we use $\preceq_1$ to provide a new characterization of the ubiquitous ordinal $\epsilon _{0}$

Categories

Keywords

Reprint years

DOI

10.1007/s001530050150

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,202

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

Assignment of Ordinals to Patterns of Resemblance.Gunnar Wilken - 2007 - Journal of Symbolic Logic 72 (2):704 - 720.
Normal forms for elementary patterns.Timothy J. Carlson & Gunnar Wilken - 2012 - Journal of Symbolic Logic 77 (1):174-194.
The Bachmann-Howard Structure in Terms of Σ1-Elementarity.Gunnar Wilken - 2006 - Archive for Mathematical Logic 45 (7):807-829.
Ordinal arithmetic with simultaneously defined theta‐functions.Andreas Weiermann & Gunnar Wilken - 2011 - Mathematical Logic Quarterly 57 (2):116-132.
Dynamic ordinal analysis.Arnold Beckmann - 2003 - Archive for Mathematical Logic 42 (4):303-334.
Reverse Mathematics and Ordinal Multiplication.Jeffry L. Hirst - 1998 - Mathematical Logic Quarterly 44 (4):459-464.
An ordinal analysis of parameter free Π12-comprehension.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (3):263-362.
Proof theory and ordinal analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.
Second-order characterizable cardinals and ordinals.Benjamin R. George - 2006 - Studia Logica 84 (3):425 - 449.
Operating on the universe.Narciso Garcia - 1988 - Archive for Mathematical Logic 27 (1):61-68.
Systems of iterated projective ordinal notations and combinatorial statements about binary labeled trees.L. Gordeev - 1989 - Archive for Mathematical Logic 29 (1):29-46.
Ordinal analysis without proofs.Jeremy Avigad - manuscript
Recent Advances in Ordinal Analysis: Π 1 2 — CA and Related Systems. [REVIEW]Michael Rathjen - 1995 - Bulletin of Symbolic Logic 1 (4):468-485.
Recent Advances in Ordinal Analysis: Π 1 2 — CA and Related Systems. [REVIEW]Michael Rathjen - 1995 - Bulletin of Symbolic Logic 1 (4):468-485.

Analytics

Added to PP
2013-11-23

Downloads
20 (#723,940)

6 months
9 (#250,037)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Elementary patterns of resemblance.Timothy J. Carlson - 2001 - Annals of Pure and Applied Logic 108 (1-3):19-77.
Patterns of resemblance of order 2.Timothy J. Carlson - 2009 - Annals of Pure and Applied Logic 158 (1-2):90-124.
The Bachmann-Howard Structure in Terms of Σ1-Elementarity.Gunnar Wilken - 2006 - Archive for Mathematical Logic 45 (7):807-829.
A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
Σ 1 -elementarity and Skolem hull operators.Gunnar Wilken - 2007 - Annals of Pure and Applied Logic 145 (2):162-175.

View all 15 citations / Add more citations

References found in this work

No references found.

Add more references