Results for 'Peter Koepke'

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  1. The consistency strength of the free-subset property for ωω.Peter Koepke - 1984 - Journal of Symbolic Logic 49 (4):1198 - 1204.
  2. Turing computations on ordinals.Peter Koepke - 2005 - 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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  3.  47
    Register computations on ordinals.Peter Koepke & Ryan Siders - 2008 - 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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  4.  18
    Ordinal machines and admissible recursion theory.Peter Koepke & Benjamin Seyfferth - 2009 - Annals of Pure and Applied Logic 160 (3):310-318.
    We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the (...)
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  5.  45
    A minimal Prikry-type forcing for singularizing a measurable cardinal.Peter Koepke, Karen Räsch & Philipp Schlicht - 2013 - 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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  6.  40
    Superatomic Boolean algebras constructed from morasses.Peter Koepke & Juan Carlos Martínez - 1995 - 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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  7.  12
    Some applications of short core models.Peter Koepke - 1988 - Annals of Pure and Applied Logic 37 (2):179-204.
    We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals . The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ω ω , and (...)
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  8.  18
    On the consistency strength of ‘Accessible’ Jonsson Cardinals and of the Weak Chang Conjecture.Hans-Dieter Donder & Peter Koepke - 1983 - Annals of Pure and Applied Logic 25 (3):233-261.
  9.  26
    On the free subset property at singular cardinals.Peter Koepke - 1989 - 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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  10.  83
    The basic theory of infinite time register machines.Merlin Carl, Tim Fischbach, Peter Koepke, Russell Miller, Miriam Nasfi & Gregor Weckbecker - 2010 - 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 (...)
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  11.  51
    Extenders, Embedding Normal Forms, and the Martin-Steel-Theorem.Peter Koepke - 1998 - 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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  12.  25
    Towards a theory of infinite time Blum-Shub-Smale machines.Peter Koepke & Benjamin Seyfferth - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 405--415.
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  13.  19
    Global square and mutual stationarity at the ℵn.Peter Koepke & Philip D. Welch - 2011 - Annals of Pure and Applied Logic 162 (10):787-806.
    We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...)
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  14.  29
    Homogeneously Souslin sets in small inner models.Peter Koepke & Ralf Schindler - 2006 - 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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  15.  52
    On the elimination of Malitz quantifiers over Archimedian real closed fields.Peter Koepke - 1989 - Archive for Mathematical Logic 28 (3):167-171.
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  16.  88
    The category of inner models.Peter Koepke - 2002 - Synthese 133 (1-2):275 - 303.
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  17.  8
    The Consistency Strength of the Free-Subset Property for $omega_omega$.Peter Koepke - 1984 - Journal of Symbolic Logic 49 (4):1198-1204.
  18.  50
    Hyperfine Structure Theory and Gap 1 Morasses.Sy-David Friedman, Peter Koepke & Boris Piwinger - 2006 - 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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  19.  19
    Regularity of Ultrafilters and the Core Model.Hans-Dieter Donder, Peter Koepke, Jean-Pierre Levinski & D. J. Walker - 1990 - Journal of Symbolic Logic 55 (3):1313-1315.
  20. Covering Properties of Core Models.Ernest Schimmerling, Peter Koepke, William J. Mitchell & John R. Steel - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  21.  64
    Making all cardinals almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - 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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  22.  53
    The consistency strength of choiceless failures of SCH.Arthur W. Apter & Peter Koepke - 2010 - 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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  23.  32
    An elementary approach to the fine structure of L.Sy D. Friedman & Peter Koepke - 1997 - Bulletin of Symbolic Logic 3 (4):453-468.
    We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...)
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  24.  31
    The Consistency Strength of $$\aleph{\omega}$$ and $$\aleph_{{\omega}1}$$ Being Rowbottom Cardinals Without the Axiom of Choice.Arthur W. Apter & Peter Koepke - 2006 - 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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  25.  8
    On the Consistency Strength of `Accessible' Jonsson Cardinals and of the Weak Chang Conjecture.Some Applications of Short Core Models.Hans-Dieter Donder & Peter Koepke - 1989 - Journal of Symbolic Logic 54 (4):1496-1497.
  26.  20
    to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a union L=⋃.Sy D. Friedman & Peter Koepke - 1997 - Bulletin of Symbolic Logic 3 (4):453-468.
    We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...)
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  27. The Consistency Strength of InlineEquation ID=" IEq1"> EquationSource Format=" TEX"> ImageObject Color=" BlackWhite" FileRef=" 15320065ArticleIEq1. gif" Format=" GIF" Rendition=" HTM" Type=" Linedraw"/> and. [REVIEW]Arthur W. Apter & Peter Koepke - 2006 - Archive for Mathematical Logic 45 (6):721-738.
  28.  10
    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]Sy D. Friedman & Peter Koepke - 1997 - Bulletin of Symbolic Logic 3 (4):453-468.
    We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...)
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  29.  21
    All uncountable cardinals in the Gitik model are almost Ramsey and carry Rowbottom filters.Arthur W. Apter, Ioanna M. Dimitriou & Peter Koepke - 2016 - Mathematical Logic Quarterly 62 (3):225-231.
    Using the analysis developed in our earlier paper, we show that every uncountable cardinal in Gitik's model of in which all uncountable cardinals are singular is almost Ramsey and is also a Rowbottom cardinal carrying a Rowbottom filter. We assume that the model of is constructed from a proper class of strongly compact cardinals, each of which is a limit of measurable cardinals. Our work consequently reduces the best previously known upper bound in consistency strength for the theory math formula (...)
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  30.  21
    The first measurable cardinal can be the first uncountable regular cardinal at any successor height.Arthur W. Apter, Ioanna M. Dimitriou & Peter Koepke - 2014 - Mathematical Logic Quarterly 60 (6):471-486.
  31.  29
    Hans-Dieter Donder and Peter Koepke. On the consistency strength of ‘accessible’ Jonsson cardinals and of the weak Chang conjecture. Annals of pure and applied logic, vol. 25 , pp. 233–261. - Peter Koepke. Some applications of short core models. Annals of pure and applied logic, vol. 37 , pp. 179–204. [REVIEW]Sy D. Friedman - 1989 - Journal of Symbolic Logic 54 (4):1496-1497.
  32.  18
    Review: Hans-Dieter Donder, Peter Koepke, On the Consistency Strength of `Accessible' Jonsson Cardinals and of the Weak Chang Conjecture; Peter Koepke, Some Applications of Short Core Models. [REVIEW]Sy D. Friedman - 1989 - Journal of Symbolic Logic 54 (4):1496-1497.
  33.  17
    Ernest Schimmerling. Covering properties of core models. Sets and proofs. (Leeds, 1997), London Mathematical Society Lecture Note Series 258. Cambridge University Press, Cambridge, 1999, pp. 281–299. - Peter Koepke. An introduction to extenders and core models for extender sequences. Logic Colloquium '87 (Granada, 1987), Studies in Logic and the Foundations of Mathematics 129. North-Holland, Amsterdam, 1989, pp. 137–182. - William J. Mitchell. The core model up to a Woodin cardinal. Logic, methodology and philosophy of science, IX (Uppsala, 1991), Studies in Logic and the Foundations of Mathematics 134, North-Holland, Amsterdam, 1994, pp. 157–175. - Benedikt Löwe and John R. Steel. An introduction to core model theory. Sets and proofs (Leeds, 1997), London Mathematical Society Lecture Note Series 258, Cambridge University Press, Cambridge, 1999, pp. 103–157. - John R. Steel. Inner models with many Woodin cardinals. Annals of Pure and Applied Logic, vol. 65 no. 2 (1993), pp. 185–209. -.Martin Zeman - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
  34.  12
    Ernest Schimmerling. Covering properties of core models. Sets and proofs. , London Mathematical Society Lecture Note Series 258. Cambridge University Press, Cambridge, 1999, pp. 281–299. - Peter Koepke. An introduction to extenders and core models for extender sequences. Logic Colloquium '87 , Studies in Logic and the Foundations of Mathematics 129. North-Holland, Amsterdam, 1989, pp. 137–182. - William J. Mitchell. The core model up to a Woodin cardinal. Logic, methodology and philosophy of science, IX , Studies in Logic and the Foundations of Mathematics 134, North-Holland, Amsterdam, 1994, pp. 157–175. - Benedikt Löwe and John R. Steel. An introduction to core model theory. Sets and proofs , London Mathematical Society Lecture Note Series 258, Cambridge University Press, Cambridge, 1999, pp. 103–157. - John R. Steel. Inner models with many Woodin cardinals. Annals of Pure and Applied Logic, vol. 65 no. 2 , pp. 185–209. - Ernest Schimmerling. Combinatorial principles in the core mode. [REVIEW]Martin Zeman - 2004 - Bulletin of Symbolic Logic 10 (4):583-588.
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  35.  11
    Review: Hans-Dieter Donder, Regularity of Ultrafilters and the Core Model; Hans-Dieter Donder, Peter Koepke, Jean-Pierre Levinski, Some Stationary Subsets of $mathscr{P}(lambda)$; D. J. Walker, On the Transversal Hypothesis and the Weak Kurepa Hypothesis. [REVIEW]Stewart Baldwin - 1990 - Journal of Symbolic Logic 55 (3):1313-1315.
  36.  23
    Donder Hans-Dieter. Regularity of ultrafilters and the core model. Israel journal of mathematics, vol. 63 , pp. 289–322. - Donder Hans-Dieter, Koepke Peter, and Levinski Jean-Pierre. Some stationary subsets of P. Proceedings of the American Mathematical Society, vol. 102 , pp. 1000–1004. - Walker D. J.. On the transversal hypothesis and the weak Kurepa hypothesis. The journal of symbolic logic, vol. 53 , pp. 854–877. [REVIEW]Stewart Baldwin - 1990 - Journal of Symbolic Logic 55 (3):1313-1315.
  37.  39
    Andrzej Walicki i \\\"warszawska szkoła historyków (historii) idei\".Ireneusz Koepke - 2005 - Filo-Sofija 5 (1(5)):259-276.
    Author: Koepke Ireneusz Title: ANDRZEJ WALICKI AND “WARSAW SCHOOL OF THE HISTORY OF IDEAS” (Andrzej Walicki i „warszawska szkoła historyków (historii) idei”) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 259-276 Keywords: ANDRZEJ WALICKI, WARSAW SCHOOL OF THE HISTORY OF IDEAS Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:This article is an attempt of presenting Andrzej Walicki connections with the so called Warsaw School of the History of Ideas and his research (...)
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  38.  7
    Nemesis und Geschichtsdialektik?Wulf Koepke - 1990 - In Kurt Mueller-Vollmer (ed.), Herder Today: Contributions From the International Herder Conference, November 5–8, 1987, Stanford, California. New York: De Gruyter. pp. 85-96.
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  39.  40
    Meaning and Mental Representation.Peter Carruthers - 1990 - Philosophical Quarterly 40 (161):527-530.
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  40. Moral realism.Peter Railton - 1986 - Philosophical Review 95 (2):163-207.
  41.  5
    Metz’s conception of African communal ethics, global economic practices and decolonisation.Peter Mwipikeni - 2024 - South African Journal of Philosophy 43 (1):94-105.
    Metz holds that we can use African communal ethics to constitute global economic practices such as appropriation, production, distribution and consumption in such a way that promotes harmonious relations. In this article, I will show that Metz’s reformist approach to constituting the global economic practices is problematic as it fails to deal with the fundamental problem that pertains to a racialised world order that is structurally configured by coloniality of being. I will show that reformist approaches such as Metz’s use (...)
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  42. Alienation, consequentialism, and the demands of morality.Peter Railton - 1984 - Philosophy and Public Affairs 13 (2):134-171.
    The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected].
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  43.  4
    Archibald Marshall’s “Motley Mixture of Crying Contradictions”: Upsidonia as Utopian Farce.Peter W. Sinnema - 2024 - Utopian Studies 34 (3):418-435.
    Abstractabstract:Karl Marx’s acerbic observation in the opening lines of The Eighteenth Brumaire that “all facts and personages of great importance in world history occur the first time as tragedy, the second as farce” may be profitably applied to a reconsideration of literary farce sui generis, a genre represented in this article by a long-neglected work of utopian fiction, Archibald Marshall’s Upsidonia (1915). Although Upsidonia’s current disregard is arguably undeserved, the article’s chief interest is not to reclaim the novel on aesthetic (...)
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  44. .Peter Railton - 1985 - Rowman & Littlefield.
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  45.  1
    Heidegger: a critical introduction.Peter Trawny - 2016 - Medford, MA: Polity. Edited by Rodrigo Therezo.
    This introduction by leading scholar Peter Trawny is the first to tackle the Black Notebooks, whose recent publication revealed the extent of Heidegger's anti-Semitism. Trawny directly confronts the most problematic aspects of Heidegger's thought, also fully surveying his work, from early writings to his magnum opus, Being and Time.
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  46. On personality.Peter Goldie - 2004 - New York: Routledge.
    The pervasiveness of personality -- Good and bad people : a question of character -- The fragility of character -- Character, responsibility and circumspection -- personality, narrative and living a life.
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  47. The book of evidence.Peter Achinstein - 2001 - New York: Oxford University Press.
    What is required for something to be evidence for a hypothesis? In this fascinating, elegantly written work, distinguished philosopher of science Peter Achinstein explores this question, rejecting typical philosophical and statistical theories of evidence. He claims these theories are much too weak to give scientists what they want--a good reason to believe--and, in some cases, they furnish concepts that mistakenly make all evidential claims a priori. Achinstein introduces four concepts of evidence, defines three of them by reference to "potential" (...)
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  48.  21
    A Contrastive Transformational Grammar: Arabic and English.Peter Abboud & Muhammad Ali Al-Khuli - 1982 - Journal of the American Oriental Society 102 (1):217.
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  49.  9
    A Dictionary of Nigerian Arabic.Peter Abboud & Alan S. Kaye - 1987 - Journal of the American Oriental Society 107 (1):184.
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  50.  20
    Aesthetic Education: A Small Manifesto.Peter Abbs - 1989 - The Journal of Aesthetic Education 23 (4):75.
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