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The Bachmann-Howard Structure in Terms of Σ1-Elementarity

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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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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 130 Math Tower, 231 W 18th Avenue, Columbus, OH, 43210, USA

    Gunnar Wilken

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  1. Gunnar Wilken
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Correspondence to Gunnar Wilken.

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The content of this article is part of the author’s Ph.D. Thesis, see [13], that was written at the Westfälische Wilhelms-Universität Münster under supervision of Professor Wolfram Pohlers. This extensive rewrite was supported by a grant from the Samuel B. Davis Fund for Mathematical Logic at the Ohio State University

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Wilken, G. The Bachmann-Howard Structure in Terms of Σ1-Elementarity. Arch. Math. Logic 45, 807–829 (2006). https://doi.org/10.1007/s00153-006-0010-6

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