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  1. Peter Päppinghaus (1989). Ptykes in GödelsT Und Definierbarkeit von Ordinalzahlen. Archive for Mathematical Logic 28 (2):119-141.
    We prove two of the inequalities needed to obtain the following result on the ordinal values of ptykes of type 2, which are definable in Gödel'sT. LetG be a dilator satisfyingG(0)=ω, ∀x:G(x)≧x, and ∀η<Ω:G(η)<Ω, and letg be the ordinal function induced byG. Then sup{A(G)∣A ptyx of type 2 definable in Gödel'sT} = sup{x∣x is∑ 1 g -definable without parameters provably in KP(G)} =J (2 +Id) g (ω) (0) = the “Bachmann-Howard ordinal relative tog”. KP(G) is obtained from Kripke-Platek set theory (...)
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  2. Peter Päppinghaus (1989). Rekursion Über Dilatoren Und Die Bachmann-Hierarchie. Archive for Mathematical Logic 28 (1):57-73.
    A hierarchy (J D g ) D Dilator of ordinal functionsJ D g : On→On is introduced and studied. It is a hierarchy of iterations relative to some giveng:OnarOn, defined by primitive recursion on dilators. This hierarchy is related to a Bachmann hierarchy $\left( {\phi _\alpha ^g } \right)_{\alpha< \varepsilon _{\Omega {\mathbf{ }} + {\mathbf{ }}1} }$ , which is built on an iteration ofg ↑ Ω as initial function.This Bachmann hierarchy $\left( {\phi _\alpha ^g } \right)_{\alpha< \varepsilon _{\Omega {\mathbf{ (...)
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  3. Peter Päppinghaus (1985). A Typed Λ-Calculus and Girard's Model of Ptykes. In G. Dorn & P. Weingarten (eds.), Foundations of Logic and Linguistics. Problems and Solutions. Plenum. 245--279.
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  4. Hans-Georg Carstens & Peter Päppinghaus (1983). Recursive Coloration of Countable Graphs. Annals of Pure and Applied Logic 25 (1):19-45.
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  5. Peter Päppinghaus & Martin Wirsing (1983). Nondeterministic Three-Valued Logic: Isotonic and Guarded Truth-Functions. Studia Logica 42 (1):1 - 22.
    Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T (true), F (false), U (undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four basic properties, called (...)
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  6. Jean-Yves Girard & Peter Päppinghaus (1981). A Result on Implications of Σ1-Sentences and its Application to Normal Form Theorems. Journal of Symbolic Logic 46 (3):634 - 642.
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