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  1. Arthur W. Apter, Ioanna M. Dimitriou & Peter Koepke (2014). The First Measurable Cardinal Can Be the First Uncountable Regular Cardinal at Any Successor Height. Mathematical Logic Quarterly 60 (6):471-486.
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  2. Peter Koepke, Karen Räsch & Philipp Schlicht (2013). A Minimal Prikry-Type Forcing for Singularizing a Measurable Cardinal. Journal of Symbolic Logic 78 (1):85-100.
    Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by $\mathscr{P}(\omega)/\mathrm{finite}$. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are \emph{no} intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality (...)
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  3. Peter Koepke & Benjamin Seyfferth (2012). Towards a Theory of Infinite Time Blum-Shub-Smale Machines. In S. Barry Cooper (ed.), How the World Computes. 405--415.
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  4. Peter Koepke & Philip D. Welch (2011). Global Square and Mutual Stationarity at the ℵn. Annals of Pure and Applied Logic 162 (10):787-806.
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  5. Arthur W. Apter & Peter Koepke (2010). The Consistency Strength of Choiceless Failures of SCH. Journal of Symbolic Logic 75 (3):1066-1080.
    We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom of Choice (AC). By the new notion of parallel Prikry forcing that we introduce, we obtain surjective failures of SCH using only one measurable cardinal, including a surjective failure of Shelah's pcf theorem about the size of the power set of $\aleph _{\omega}$ . Using symmetric collapses to $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ , (...)
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  6. Merlin Carl, Tim Fischbach, Peter Koepke, Russell Miller, Miriam Nasfi & Gregor Weckbecker (2010). The Basic Theory of Infinite Time Register Machines. Archive for Mathematical Logic 49 (2):249-273.
    Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is set (...)
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  7. Peter Koepke & Benjamin Seyfferth (2009). Ordinal Machines and Admissible Recursion Theory. Annals of Pure and Applied Logic 160 (3):310-318.
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  8. Arthur W. Apter & Peter Koepke (2008). Making All Cardinals Almost Ramsey. Archive for Mathematical Logic 47 (7-8):769-783.
    We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions, we construct a model of ZF + ${\neg {\rm AC}_\omega}$ in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals, we can weaken this to an equiconsistency of the following theories: “ZFC + There is a proper class of regular almost (...)
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  9. Peter Koepke & Ryan Siders (2008). Register Computations on Ordinals. Archive for Mathematical Logic 47 (6):529-548.
    We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register (...)
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  10. Arthur W. Apter & Peter Koepke (2006). The Consistency Strength of Aleph{Omega} and Aleph_{{Omega}1} Being Rowbottom Cardinals Without the Axiom of Choice. Archive for Mathematical Logic 45 (6):721-737.
    We show that for all natural numbers n, the theory “ZF + DC $_{\aleph_n}$ + $\aleph_{\omega}$ is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + $\aleph_{\omega_1}$ is an ω 2-Rowbottom cardinal carrying an ω 2-Rowbottom filter and ω 1 is regular” has the same consistency strength as the theory “ZFC + There exist ω 1 measurable cardinals”. We (...)
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  11. Arthur W. Apter & Peter Koepke (2006). The Consistency Strength of InlineEquation ID=" IEq1"> EquationSource Format=" TEX"> ImageObject Color=" BlackWhite" FileRef=" 15320065ArticleIEq1. Gif" Format=" GIF" Rendition=" HTM" Type=" Linedraw"/> And. [REVIEW] Archive for Mathematical Logic 45 (6):721-738.
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  12. Sy-David Friedman, Peter Koepke & Boris Piwinger (2006). Hyperfine Structure Theory and Gap 1 Morasses. Journal of Symbolic Logic 71 (2):480 - 490.
    Using the Friedman-Koepke Hyperfine Structure Theory of [2], we provide a short construction of a gap 1 morass in the constructible universe.
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  13. Peter Koepke & Ralf Schindler (2006). Homogeneously Souslin Sets in Small Inner Models. Archive for Mathematical Logic 45 (1):53-61.
    We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K, where K is the core model below a μ-measurable cardinal.
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  14. Peter Koepke (2005). Turing Computations on Ordinals. Bulletin of Symbolic Logic 11 (3):377-397.
    We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.
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  15. Peter Koepke (2002). The Category of Inner Models. Synthese 133 (1-2):275 - 303.
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  16. Peter Koepke (1998). Extenders, Embedding Normal Forms, and the Martin-Steel-Theorem. Journal of Symbolic Logic 63 (3):1137-1176.
    We propose a simple notion of "extender" for coding large elementary embeddings of models of set theory. As an application we present a self-contained proof of the theorem by D. Martin and J. Steel that infinitely many Woodin cardinals imply the determinacy of every projective set.
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  17. Sy D. Friedman & Peter Koepke (1997). An Elementary Approach to the Fine Structure of L. Bulletin of Symbolic Logic 3 (4):453-468.
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  18. Syd Friedman & Peter Koepke (1997). To Show the Relative Consistency of Cantor's Continuum Hypothesis. L is Defined as a Union L=⋃. Bulletin of Symbolic Logic 3 (4).
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  19. Syd Friedman & Peter Koepke (1997). X1. Introduction. In 1938, K. Gödel Defined the Model L of Set Theory to Show the Relative Consistency of Cantor's Continuum Hypothesis. L is Defined as a Union L=. [REVIEW] Bulletin of Symbolic Logic 3 (4).
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  20. Peter Koepke & Juan Carlos Martínez (1995). Superatomic Boolean Algebras Constructed From Morasses. Journal of Symbolic Logic 60 (3):940-951.
    By using the notion of a simplified (κ,1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.
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  21. Peter Koepke (1989). On the Elimination of Malitz Quantifiers Over Archimedian Real Closed Fields. Archive for Mathematical Logic 28 (3):167-171.
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  22. Peter Koepke (1989). On the Free Subset Property at Singular Cardinals. Archive for Mathematical Logic 28 (1):43-55.
    We give a proof ofTheorem 1. Let κ be the smallest cardinal such that the free subset property Fr ω (κ,ω 1)holds. Assume κ is singular. Then there is an inner model with ω1 measurable cardinals.
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  23. Peter Koepke (1988). Some Applications of Short Core Models. Annals of Pure and Applied Logic 37 (2):179-204.
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  24. Peter Koepke (1984). The Consistency Strength of the Free-Subset Property for Ωω. Journal of Symbolic Logic 49 (4):1198 - 1204.
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  25. Peter Koepke (1984). The Consistency Strength of the Free-Subset Property for $Omega_omega$. Journal of Symbolic Logic 49 (4):1198-1204.
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  26. Hans-Dieter Donder & Peter Koepke (1983). On the Consistency Strength of 'Accessible' Jonsson Cardinals and of the Weak Chang Conjecture. Annals of Pure and Applied Logic 25 (3):233-261.
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