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  1. Andrey Bovykin & Andreas Weiermann (forthcoming). The Strength of Infinitary Ramseyan Principles Can Be Accessed by Their Densities. Annals of Pure and Applied Logic.
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  2. Sy-David Friedman, Michael Rathjen & Andreas Weiermann (2013). Slow Consistency. Annals of Pure and Applied Logic 164 (3):382-393.
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  3. 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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  4. Michiel De Smet & Andreas Weiermann (2012). Goodstein Sequences for Prominent Ordinals Up to the Bachmann–Howard Ordinal. Annals of Pure and Applied Logic 163 (6):669-680.
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  5. Lev Gordeev & Andreas Weiermann (2012). Phase Transitions of Iterated Higman-Style Well-Partial-Orderings. Archive for Mathematical Logic 51 (1-2):127-161.
    We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo ${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$ in question, d > 1, we fix a natural extension of Peano Arithmetic, ${T \supseteq \sf{PA}}$ , that proves the corresponding second-order sentence ${\sf{WPO}\left({\rm S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$ . Having this we consider the following parametrized first-order slow well-partial-ordering sentence ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$ $$\left( \forall K > 0 (...)
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  6. Lars Kristiansen, Jan-Christoph Schlage-Puchta & Andreas Weiermann (2012). Streamlined Subrecursive Degree Theory. Annals of Pure and Applied Logic 163 (6):698-716.
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  7. Andreas Weiermann & Alan R. Woods (2012). Some Natural Zero One Laws for Ordinals Below Ε 0. In. In S. Barry Cooper (ed.), How the World Computes. 723--732.
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  8. Michael Rathjen & Andreas Weiermann (2011). Reverse Mathematics and Well-Ordering Principles. In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific.
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  9. Andreas Weiermann & Gunnar Wilken (2011). Ordinal Arithmetic with Simultaneously Defined Theta‐Functions. Mathematical Logic Quarterly 57 (2):116-132.
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  10. Eran Omri & Andreas Weiermann (2009). Classifying the Phase Transition Threshold for Ackermannian Functions. Annals of Pure and Applied Logic 158 (3):156-162.
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  11. Andreas Weiermann (2009). Phase Transitions for Gödel Incompleteness. Annals of Pure and Applied Logic 157 (2):281-296.
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  12. Henryk Kotlarski, Bożena Piekart & Andreas Weiermann (2007). More on Lower Bounds for Partitioning Α-Large Sets. Annals of Pure and Applied Logic 147 (3):113-126.
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  13. Andreas Weiermann (2007). Phase Transition Thresholds for Some Friedman-Style Independence Results. Mlq 53 (1):4-18.
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  14. Steve Awodey, Raf Cluckers, Ilijas Farah, Solomon Feferman, Deirdre Haskell, Andrey Morozov, Vladimir Pestov, Andre Scedrov, Andreas Weiermann & Jindrich Zapletal (2006). Stanford University, Stanford, CA March 19–22, 2005. Bulletin of Symbolic Logic 12 (1).
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  15. Andreas Weiermann (2006). Classifying the Provably Total Functions of Pa. Bulletin of Symbolic Logic 12 (2):177-190.
    We give a self-contained and streamlined version of the classification of the provably computable functions of PA. The emphasis is put on illuminating as well as seems possible the intrinsic computational character of the standard cut elimination process. The article is intended to be suitable for teaching purposes and just requires basic familiarity with PA and the ordinals below ε0. (Familiarity with a cut elimination theorem for a Gentzen or Tait calculus is helpful but not presupposed).
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  16. Andreas Weiermann (2005). Analytic Combinatorics, Proof-Theoretic Ordinals, and Phase Transitions for Independence Results. Annals of Pure and Applied Logic 136 (1):189-218.
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  17. Andreas Weiermann (2003). An Application of Graphical Enumeration to PA. Journal of Symbolic Logic 68 (1):5-16.
    For α less than ε0 let $N\alpha$ be the number of occurrences of ω in the Cantor normal form of α. Further let $\mid n \mid$ denote the binary length of a natural number n, let $\mid n\mid_h$ denote the h-times iterated binary length of n and let inv(n) be the least h such that $\mid n\mid_h \leq 2$ . We show that for any natural number h first order Peano arithmetic, PA, does not prove the following sentence: For all (...)
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  18. Benedikt Löwe, Florian Rudolph, Andreas Weiermann & Slow Versus Fast Growing (2002). Foundations of the Formal Sciences I. Synthese 133:463-464.
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  19. Andreas Weiermann (2002). Review: Toshiyasu Arai, Consistency Proof Via Pointwise Induction. [REVIEW] Bulletin of Symbolic Logic 8 (4):536-537.
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  20. Andreas Weiermann (2002). Slow Versus Fast Growing. Synthese 133 (1-2):13 - 29.
    We survey a selection of results about majorization hierarchies. The main focus is on classical and recent results about the comparison between the slow and fast growing hierarchies.
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  21. Andreas Weiermann (2001). Γ0 May Be Minimal Subrecursively Inaccessible. Mathematical Logic Quarterly 47 (3):397-408.
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  22. Andreas Weiermann (2001). Some Interesting Connections Between the Slow Growing Hierarchy and the Ackermann Function. Journal of Symbolic Logic 66 (2):609-628.
    It is shown that the so called slow growing hierarchy depends non trivially on the choice of its underlying structure of ordinals. To this end we investigate the growth rate behaviour of the slow growing hierarchy along natural subsets of notations for Γ 0 . Let T be the set-theoretic ordinal notation system for Γ 0 and T tree the tree ordinal representation for Γ. It is shown in this paper that (G α ) α ∈ T matches up with (...)
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  23. Arnold Beckmann & Andreas Weiermann (2000). Characterizing the Elementary Recursive Functions by a Fragment of Gödel's T. Archive for Mathematical Logic 39 (7):475-491.
    Let T be Gödel's system of primitive recursive functionals of finite type in a combinatory logic formulation. Let $T^{\star}$ be the subsystem of T in which the iterator and recursor constants are permitted only when immediately applied to type 0 arguments. By a Howard-Schütte-style argument the $T^{\star}$ -derivation lengths are classified in terms of an iterated exponential function. As a consequence a constructive strong normalization proof for $T^{\star}$ is obtained. Another consequence is that every $T^{\star}$ -representable number-theoretic function is elementary (...)
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  24. Benjamin Blankertz & Andreas Weiermann (1999). A Uniform Approach for Characterizing the Provably Total Number-Theoretic Functions of KPM and (Some of) its Subsystems. Studia Logica 62 (3):399-427.
    In this article we show how to extract with the use of the Buchholz-Cichon-Weiermann approach to subrecursive hierarchies from Rathjen's 1991 ordinal analysis of KPM a characterization of the provably total number-theoretic functions of KPM and some of its (most prominent) subsystems in a uniform and direct way.
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  25. Andreas Weiermann (1998). Bounding Derivation Lengths with Functions From the Slow Growing Hierarchy. Archive for Mathematical Logic 37 (5-6):427-441.
    Let $R$ be a (finite) rewrite system over a (finite) signature. Let $\succ$ be a strict well-founded termination ordering on the set of terms in question so that the rules of $R$ are reducing under $\succ$ . Then $R$ is terminating. In this article it is proved for a certain class of far reaching termination orderings (of order type reaching up to the first subrecursively inaccessible ordinal, i.e. the proof-theoretic ordinal of $ID_{<\omega}$ ) that – under some reasonable assumptions which (...)
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  26. Andreas Weiermann (1998). How is It That Infinitary Methods Can Be Applied to Finitary Mathematics? Gödel's T: A Case Study. Journal of Symbolic Logic 63 (4):1348-1370.
    Inspired by Pohlers' local predicativity approach to Pure Proof Theory and Howard's ordinal analysis of bar recursion of type zero we present a short, technically smooth and constructive strong normalization proof for Gödel's system T of primitive recursive functionals of finite types by constructing an ε 0 -recursive function [] 0 : T → ω so that a reduces to b implies [a] $_0 > [b]_0$ . The construction of [] 0 is based on a careful analysis of the Howard-Schütte (...)
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  27. E. A. Cichon & Andreas Weiermann (1997). Term Rewriting Theory for the Primitive Recursive Functions. Annals of Pure and Applied Logic 83 (3):199-223.
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  28. Andreas Weiermann (1997). A Proof of Strongly Uniform Termination for Gödel's T by Methods From Local Predicativity. Archive for Mathematical Logic 36 (6):445-460.
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  29. Andreas Weiermann (1997). Sometimes Slow Growing is Fast Growing. Annals of Pure and Applied Logic 90 (1-3):91-99.
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  30. Arnold Beckmann & Andreas Weiermann (1996). A Term Rewriting Characterization of the Polytime Functions and Related Complexity Classes. Archive for Mathematical Logic 36 (1):11-30.
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  31. Andreas Weiermann (1996). How to Characterize Provably Total Functions by Local Predicativity. Journal of Symbolic Logic 61 (1):52-69.
    Inspired by Pohlers' proof-theoretic analysis of KPω we give a straightforward non-metamathematical proof of the (well-known) classification of the provably total functions of $PA, PA + TI(\prec\lceil)$ (where it is assumed that the well-ordering $\prec$ has some reasonable closure properties) and KPω. Our method relies on a new approach to subrecursion due to Buchholz, Cichon and the author.
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  32. Andreas Weiermann (1995). Investigations on Slow Versus Fast Growing: How to Majorize Slow Growing Functions Nontrivially by Fast Growing Ones. [REVIEW] Archive for Mathematical Logic 34 (5):313-330.
    Let T(Ω) be the ordinal notation system from Buchholz-Schütte (1988). [The order type of the countable segmentT(Ω)0 is — by Rathjen (1988) — the proof-theoretic ordinal the proof-theoretic ordinal ofACA 0 + (Π 1 l −TR).] In particular let ↦Ω a denote the enumeration function of the infinite cardinals and leta ↦ ψ0 a denote the partial collapsing operation on T(Ω) which maps ordinals of T(Ω) into the countable segment TΩ 0 of T(Ω). Assume that the (fast growing) extended Grzegorczyk (...)
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  33. Wilfried Buchholz, Adam Cichon & Andreas Weiermann (1994). A Uniform Approach to Fundamental Sequences and Hierarchies. Mathematical Logic Quarterly 40 (2):273-286.
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  34. Andreas Weiermann (1994). A Functorial Property of the Aczel-Buchholz-Feferman Function. Journal of Symbolic Logic 59 (3):945-955.
    Let Ω be the least uncountable ordinal. Let K(Ω) be the category where the objects are the countable ordinals and where the morphisms are the strictly monotonic increasing functions. A dilator is a functor on K(Ω) which preserves direct limits and pullbacks. Let $\tau \Omega: \xi = \omega^\xi\}$ . Then τ has a unique "term"-representation in Ω. λξη.ω ξ + η and countable ordinals called the constituents of τ. Let $\delta and K(τ) be the set of the constituents of τ. (...)
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  35. Michael Rathjen & Andreas Weiermann (1993). Proof-Theoretic Investigations on Kruskal's Theorem. Annals of Pure and Applied Logic 60 (1):49-88.
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  36. Andreas Weiermann (1993). An Order‐Theoretic Characterization of the Schütte‐Veblen‐Hierarchy. Mathematical Logic Quarterly 39 (1):367-383.
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  37. Andreas Weiermann (1993). A Simplified Functorial Construction of the Veblen Hierarchy. Mathematical Logic Quarterly 39 (1):269-273.
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  38. Andreas Weiermann (1993). Bounds for the Closure Ordinals of Essentially Monotonic Increasing Functions. Journal of Symbolic Logic 58 (2):664-671.
    Let $\Omega:= \aleph_1$ . For any $\alpha \Omega:\xi = \omega^\xi\}$ let EΩ (α) be the finite set of ε-numbers below Ω which are needed for the unique representation of α in Cantor-normal form using 0, Ω, +, and ω. Let $\alpha^\ast:= \max (E_\Omega(\alpha) \cup \{0\})$ . A function f: εΩ + 1 → Ω is called essentially increasing, if for any $\alpha < \varepsilon_{\Omega + 1}; f(\alpha) \geq \alpha^\ast: f$ is called essentially monotonic, if for any $\alpha,\beta < \varepsilon_{\Omega + (...)
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  39. Andreas Weiermann (1991). Vereinfachte Kollabierungsfunktionen Und Ihre Anwendungen. Archive for Mathematical Logic 31 (2):85-94.
    In this article we define a new and transparent concept of total collapsing functions for an ordinal notation system which is characteristic for the theory (Δ 2 1 -CA)+(BI). We show that our construction allows the application of Pohler's method of local predicativity as presented in [2] which yields a perspicious proof-theoretic analysis of (Δ 2 1 -CA)+(BI) being not much more complicated than for ID1.
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