The Bachmann-Howard Structure in Terms of Σ1-Elementarity

Archive for Mathematical Logic 45 (7):807-829 (2006)
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Abstract

The Bachmann-Howard structure, that is the segment of ordinal numbers below the proof theoretic ordinal of Kripke-Platek set theory with infinity, is fully characterized in terms of CARLSON’s approach to ordinal notation systems based on the notion of Σ1-elementarity

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Citations of this work

Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
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Normal forms for elementary patterns.Timothy J. Carlson & Gunnar Wilken - 2012 - Journal of Symbolic Logic 77 (1):174-194.
Ordinal arithmetic based on Skolem hulling.Gunnar Wilken - 2007 - Annals of Pure and Applied Logic 145 (2):130-161.
Pure Σ2-elementarity beyond the core.Gunnar Wilken - 2021 - Annals of Pure and Applied Logic 172 (9):103001.

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References found in this work

Proof-theoretic investigations on Kruskal's theorem.Michael Rathjen & Andreas Weiermann - 1993 - Annals of Pure and Applied Logic 60 (1):49-88.
Proof theory and ordinal analysis.W. Pohlers - 1991 - Archive for Mathematical Logic 30 (5-6):311-376.
An ordinal analysis of parameter free Π12-comprehension.Michael Rathjen - 2005 - Archive for Mathematical Logic 44 (3):263-362.
Elementary patterns of resemblance.Timothy J. Carlson - 2001 - Annals of Pure and Applied Logic 108 (1-3):19-77.
Ordinal arithmetic and $\Sigma_{1}$ -elementarity.Timothy J. Carlson - 1999 - Archive for Mathematical Logic 38 (7):449-460.

View all 13 references / Add more references