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  1. Andreas Weiermann & Gunnar Wilken (2013). Goodstein Sequences for Prominent Ordinals Up to the Ordinal Of. Annals of Pure and Applied Logic 164 (12):1493-1506.
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  2. Timothy J. Carlson & Gunnar Wilken (2012). Normal Forms for Elementary Patterns. Journal of Symbolic Logic 77 (1):174-194.
    A notation for an ordinal using patterns of resemblance is based on choosing an isominimal set of ordinals containing the given ordinal. There are many choices for this set meaning that notations are far from unique. We establish that among all such isominimal sets there is one which is smallest under inclusion thus providing an appropriate notion of normal form notation in this context. In addition, we calculate the elements of this isominimal set using standard notations based on collapsing functions. (...)
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  3. Timothy J. Carlson & Gunnar Wilken (2012). Tracking Chains of Σ2-Elementarity. Annals of Pure and Applied Logic 163 (1):23-67.
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  4. Andreas Weiermann & Gunnar Wilken (2011). Ordinal Arithmetic with Simultaneously Defined Theta‐Functions. Mathematical Logic Quarterly 57 (2):116-132.
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  5. Gunnar Wilken (2007). Assignment of Ordinals to Patterns of Resemblance. Journal of Symbolic Logic 72 (2):704 - 720.
    In [2] T. J. Carlson introduces an approach to ordinal notation systems which is based on the notion of Σ₁-elementary substructure. We gave a detailed ordinal arithmetical analysis (see [7]) of the ordinal structure based on Σ₁-elementarity as defined in [2]. This involved the development of an appropriate ordinal arithmetic that is based on a system of classical ordinal notations derived from Skolem hull operators, see [6]. In the present paper we establish an effective order isomorphism between the classical and (...)
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  6. Gunnar Wilken (2007). Σ1-Elementarity and Skolem Hull Operators. Annals of Pure and Applied Logic 145 (2):162-175.
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  7. Gunnar Wilken (2007). Ordinal Arithmetic Based on Skolem Hulling. Annals of Pure and Applied Logic 145 (2):130-161.
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  8. Gunnar Wilken (2006). The Bachmann-Howard Structure in Terms of Σ1-Elementarity. Archive for Mathematical Logic 45 (7):807-829.
    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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