Results for 'Peter Cholak'

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  1. On the Strength of Ramsey's Theorem for Pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
    We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and BΣ (...)
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  2. A Computably Stable Structure with No Scott Family of Finitary Formulas.Peter Cholak, Richard A. Shore & Reed Solomon - 2006 - Archive for Mathematical Logic 45 (5):519-538.
  3.  11
    Automorphisms of the Lattice of Recursively Enumerable Sets.Peter Cholak - 1995 - American Mathematical Society.
    Chapter 1: Introduction. S = <{We}c<w; C,U,n,0,w> is the substructure formed by restricting the lattice <^P(w); C , U, n,0,w> to the re subsets We of the ...
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  4.  12
    Reverse Mathematics and the Equivalence of Definitions for Well and Better Quasi-Orders.Peter Cholak, Alberto Marcone & Reed Solomon - 2004 - Journal of Symbolic Logic 69 (3):683-712.
  5.  9
    Computably Categorical Structures and Expansions by Constants.Peter Cholak, Sergey Goncharov, Bakhadyr Khoussainov & Richard A. Shore - 1999 - Journal of Symbolic Logic 64 (1):13-37.
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  6.  14
    Uniform Almost Everywhere Domination.Peter Cholak, Noam Greenberg & Joseph S. Miller - 2006 - Journal of Symbolic Logic 71 (3):1057 - 1072.
    We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.
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  7.  15
    On the Definability of the Double Jump in the Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2002 - Journal of Mathematical Logic 2 (02):261-296.
  8.  42
    An Almost Deep Degree.Peter Cholak, Marcia Groszek & Theodore Slaman - 2001 - Journal of Symbolic Logic 66 (2):881-901.
    We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.).
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  9.  3
    On Mathias Generic Sets.Peter A. Cholak, Damir D. Dzhafarov & Jeffry L. Hirst - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 129--138.
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  10.  26
    Definable Encodings in the Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2000 - Bulletin of Symbolic Logic 6 (2):185-196.
  11.  14
    The Complexity of Orbits of Computably Enumerable Sets.Peter A. Cholak, Rodney Downey & Leo A. Harrington - 2008 - Bulletin of Symbolic Logic 14 (1):69 - 87.
    The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...)
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  12.  12
    On the Cantor-Bendixon Rank of Recursively Enumerable Sets.Peter Cholak & Rod Downey - 1993 - Journal of Symbolic Logic 58 (2):629-640.
    The main result of this paper is to show that for every recursive ordinal α ≠ 0 and for every nonrecursive r.e. degree d there is a r.e. set of rank α and degree d.
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  13.  16
    The Translation Theorem.Peter Cholak - 1994 - Archive for Mathematical Logic 33 (2):87-108.
    We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.
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  14.  5
    Some Orbits for E.Peter Cholak, Rod Downey & Eberhard Herrmann - 2001 - Annals of Pure and Applied Logic 107 (1-3):193-226.
    In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.
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  15.  15
    Iterated Relative Recursive Enumerability.Peter A. Cholak & Peter G. Hinman - 1994 - Archive for Mathematical Logic 33 (5):321-346.
    A result of Soare and Stob asserts that for any non-recursive r.e. setC, there exists a r.e.[C] setA such thatA⊕C is not of r.e. degree. A setY is called [of]m-REA (m-REA[C] [degree] iff it is [Turing equivalent to] the result of applyingm-many iterated ‘hops’ to the empty set (toC), where a hop is any function of the formX→X ⊕W e X . The cited result is the special casem=0,n=1 of our Theorem. Form=0,1, and any (m+1)-REA setC, ifC is not ofm-REA (...)
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  16.  17
    The Dense Simple Sets Are Orbit Complete with Respect to the Simple Sets.Peter Cholak - 1998 - Annals of Pure and Applied Logic 94 (1-3):37-44.
    We prove conjectures of Herrmann and Stob by showing that the dense simple sets are orbit complete w.r.t. the simple sets.
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  17.  20
    Maximal Contiguous Degrees.Peter Cholak, Rod Downey & Stephen Walk - 2002 - Journal of Symbolic Logic 67 (1):409-437.
    A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...)
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  18.  6
    Introduction to the Special Issue on Vaught's Conjecture.Peter Cholak - 2007 - Notre Dame Journal of Formal Logic 48 (1):1-2.
  19.  20
    Isomorphisms of Splits of Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2003 - Journal of Symbolic Logic 68 (3):1044-1064.
    We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
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  20.  6
    Lattice Nonembeddings and Intervals of the Recursively Enumerable Degrees.Peter Cholak & Rod Downey - 1993 - Annals of Pure and Applied Logic 61 (3):195-221.
    Let b and c be r.e. Turing degrees such that b>c. We show that there is an r.e. degree a such that b>a>c and all lattices containing a critical triple, including the lattice M5, cannot be embedded into the interval [c, a].
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  21.  14
    Boolean Algebras and Orbits of the Lattice of R.E. Sets Modulo the Finite Sets.Peter Cholak - 1990 - Journal of Symbolic Logic 55 (2):744-760.
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    Participants and Titles of Lectures.Klaus Ambos-Spies, Marat Arslanov, Douglas Cenzer, Peter Cholak, Chi Tat Chong, Decheng Ding, Rod Downey, Peter A. Fejer, Sergei S. Goncharov & Edward R. Griffor - 1998 - Annals of Pure and Applied Logic 94 (1):3-6.
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  23.  4
    Reverse Mathematics and Infinite Traceable Graphs.Peter Cholak, David Galvin & Reed Solomon - 2012 - Mathematical Logic Quarterly 58 (1-2):18-28.
    We analyze three applications of Ramsey’s Theorem for 4-tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey’s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA0.
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  24.  1
    Simpson Stephen G.. Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic. Springer, Berlin, Heidelberg, New York, Etc., 1999, Xiv + 445 Pp. [REVIEW]Peter Cholak - 1999 - Journal of Symbolic Logic 64 (3):1356-1357.
  25.  1
    Corrigendum To: “On the Strength of Ramsey's Theorem for Pairs”.Peter Cholak, Jr} {Jockusch & Theodore A. Slaman - 2009 - Journal of Symbolic Logic 74 (4):1438-1439.
  26.  1
    Review: Stephen G. Simpson, Subsystems of Second Order Arithmetic. [REVIEW]Peter Cholak - 1999 - Journal of Symbolic Logic 64 (3):1356-1357.
  27. ${\Cal D}$-Maximal Sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
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  28. On N -Tardy Sets.Peter A. Cholak, Peter M. Gerdes & Karen Lange - 2012 - Annals of Pure and Applied Logic 163 (9):1252-1270.
  29.  32
    Peter Singer on Global Ethics.Madsen Peter - 2004 - Business Ethics Quarterly 14 (1):183-196.
  30.  17
    Donatella Di Cesare: Heidegger, Die Juden, Die Shoah Und Peter Trawny, Andrew J. Mitchell : Heidegger, Die Juden, Noch Einmal.Donatella Di Cesare, Trawny Peter, Andrew J. Mitchell & Reinhard Mehring - 2016 - Philosophischer Literaturanzeiger 69 (2):137-146.
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  31.  16
    Péter Rózsa. Rekurzív Definiciók, Melyek Változó Számu Korábbi Függvényertéket Használnak Fel. Matematikai Lapok , Vol. 5 , Pp. 7–9. An Abstract of XX 176.Péter Rózsa. Ujabb Bizonyítás Arra, Hogy a Csillag-Kalmár-Féle Elemi Függvények Osztálya Szükebb, Mint a Primitiv-Rekurzív Függvényeké. Matematikai Lapok , Vol. 5 , Pp. 244–252. Hungarian Version of XX 282.Péter Rózsa. Kalmár László Matematikai Munkássága . Ebd., Bd. 6 , S. 138–150. [REVIEW]R. Péter - 1957 - Journal of Symbolic Logic 22 (3):295-296.
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    My Life with Censorship: Sís, Peter, 1949- -- Childhood and Youth.SíS. Peter - 2009 - Journal of the History of Philosophy 47 (3):42-45.
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  33. Democratic Legitimacy Without Collective Rationality Fabienne Peter.Fabienne Peter - 2009 - In Boudewijn Paul de Bruin & Christopher F. Zurn (eds.), New Waves in Political Philosophy. Palgrave-Macmillan. pp. 143.
     
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  34. Robert I. Soare. Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets. Annals of Mathematics, Ser. 2 Vol. 100 , Pp. 80–120.Manuel Lerman and Robert I. Soare. D-Simple Sets, Small Sets, and Degree Classes. Pacific Journal of Mathematics, Vol. 87 , Pp. 135–155.Peter Cholak. Automorphisms of the Lattice of Recursively Enumerable Sets. Memoirs of the American Mathematical Society, No. 541. American Mathematical Society, Providence 1995, Viii + 151 Pp.Leo Harrington and Robert I. Soare. The Δ3 0-Automorphism Method and Noninvariant Classes of Degrees. Journal of the American Mathematical Society, Vol. 9 , Pp. 617–666. [REVIEW]Rod Downey - 1997 - Journal of Symbolic Logic 62 (3):1048-1055.
  35.  2
    The Notre Dame Lectures, Edited by Cholak Peter, Lecture Notes in Logic, Vol. 18. Association for Symbolic Logic, AK Peters, Ltd., Wellesley, Massachusetts, 2005, Vii+ 185 Pp. [REVIEW]Roman Kossak - 2006 - Bulletin of Symbolic Logic 12 (4):605-607.
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  36.  1
    [Omnibus Review].Rod Downey - 1997 - Journal of Symbolic Logic 62 (3):1048-1055.
    Robert I. Soare, Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets.Manuel Lerman, Robert I. Soare, $d$-Simple Sets, Small Sets, and Degree Classes.Peter Cholak, Automorphisms of the Lattice of Recursively Enumerable Sets.Leo Harrington, Robert I. Soare, The $\Delta^0_3$-Automorphism Method and Noninvariant Classes of Degrees.
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  37. The Early Reception of Peter Auriol at Oxford.Rondo Keele - 2015 - Recherches de Theologie Et Philosophie Medievales 82:301-361.
    The important impact of the French Franciscan Peter Auriol (ca. 1280-1322) upon contemporary philosophical theology at Oxford is well known and has been well documented and analyzed, at least for a narrow range of issues, particularly in epistemology. This article attempts a more systematic treatment of his effects upon Oxford debates across a broader range of subjects and over a more expansive duration of time than has been done previously. Topics discussed include grace and merit, future contingents and divine (...)
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  38.  29
    Into Terra Incognita: Charting Beyond Peter Harrison's the Territories of Science and Religion.Michael Fuller - 2016 - Zygon 51 (3):729-741.
    Peter Harrison's The Territories of Science and Religion throws down a serious challenge to advocates of dialogue as the primary means of engagement between science and religion. This article accepts the validity of this challenge and looks at four possible responses to it. The first—a return to the past—is rejected. The remaining three—exploring new epistemic frameworks for the encounter of science and religion, broadening out the engagement beyond the context of the physical sciences and Western culture, and looking at (...)
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  39.  26
    Attention, Perceptual Content, and Mirrors: Two Medieval Models of Active Perception in Peter Olivi and Peter Auriol.Lukáš Lička - 2017 - Perception in Scholastics and Their Interlocutors.
    In the paper I argue that medieval philosophers proposed several notions of the senses’ activity in perception. I illustrate the point using the example of two Franciscan thinkers – Peter Olivi (ca. 1248–1298) and Peter Auriol (ca. 1280–1322). Olivi’s notion of active perception assumes that every perceptual act demands a prior focusing of the mind’s attention. Furthermore, Olivi is partially inspired by the extramissionist theories of vision and reinterprets the notion of a visual ray postulated by them as (...)
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  40.  45
    Peter Auriol on the Intuitive Cognition of Nonexistents. Revisiting the Charge of Skepticism in Walter Chatton and Adam Wodeham.Han Thomas Adriaenssen - 2017 - Oxford Studies in Medieval Philosophy 5:151-180.
    This paper looks at the critical reception of two central claims of Peter Auriol’s theory of cognition: the claim that the objects of cognition have an apparent or objective being that resists reduction to the real being of objects, and the claim that there may be natural intuitive cognitions of nonexistent objects. These claims earned Auriol the criticism of his fellow Franciscans, Walter Chatton and Adam Wodeham. According to them, the theory of apparent being was what had led Auriol (...)
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  41. Peter Olivi on Practical Reasoning.Juhana Toivanen - 2012 - In A. Musco (ed.), Universality of Reason, Plurality of Philosophies in the Middle Ages: Proceedings of the 12th International Congress of Medieval Philosophy (S.I.E.P.M.), vol. II-2. Palermo: Officina di Studi Medievali. pp. 1033-1045.
    The subject matter of this essay is Peter of John Olivi’s (ca.1248–98) conception of reason from the viewpoint of human action.
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  42. Truth and Paradox in Late XIVth Century Logic : Peter of Mantua’s Treatise on Insoluble Propositions.Riccardo Strobino - 2012 - Documenti E Studi Sulla Tradizione Filosofica Medievale 23:475-519.
    This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an (...)
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  43. Singer, Peter (1946-).Anthony Skelton - 2014 - In Michael Gibbons (ed.), Encyclopedia of Political Thought. Wiley-Blackwell. pp. 3454-3455.
    A short encyclopedia article on Peter Singer which discusses his views on the obligations that the global wealthy have to the global poor and on our obligations to non-human animals.
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  44.  15
    Peter Lombard on God’s Knowledge: Sententiae, Book I, Distinctions 35-38, as the Basis for Later Theological Discussions.Rostislav Tkachenko - 2017 - Sententiae 36 (1):17-30.
    Since the mid-90’s the figure of Peter Lombard and his Book of Sentences has regained the importance in scholarly world and been studied from both historical-theological and historical-philosophical perspectives. But some aspects of his thinking, encapsulated in the written form, which was to become the material basis for the thirteenth- through the fifteenth-century theological projects, remained somewhat insufficiently researched. Therefore this article analyzes the select parts of the Book of Sentences with the purpose of looking at how Peter (...)
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  45. The Active Nature of the Soul in Sense Perception: Robert Kilwardby and Peter Olivi.Juhana Toivanen & José Filipe Silva - 2010 - Vivarium 48 (3):245-278.
    This article discusses the theories of perception of Robert Kilwardby and Peter of John Olivi. Our aim is to show how in challenging certain assumptions of medieval Aristotelian theories of perception they drew on Augustine and argued for the active nature of the soul in sense perception. For both Kilwardby and Olivi, the soul is not passive with respect to perceived objects; rather, it causes its own cognitive acts with respect to external objects and thus allows the subject to (...)
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  46. Exploring Evil and Philosophical Failure: A Critical Notice of Peter van Inwagen's *The Problem of Evil.John Martin Fischer & Neal A. Tognazzini - 2007 - Faith and Philosophy 24 (4):458-474.
    In his recent book on the problem of evil, Peter van Inwagen argues that both the global and local arguments from evil are failures. In this paper, we engagevan Inwagen’s book at two main points. First, we consider his understanding of what it takes for a philosophical argument to succeed. We argue that while his criterion for success is interesting and helpful, there is good reason to think it is too stringent. Second, we consider his responses to the global (...)
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  47. Perception and Objective Being: Peter Auriol on Perceptual Acts and Their Objects.Lukáš Lička - 2016 - American Catholic Philosophical Quarterly 90 (1):49-76.
    This article discusses the theory of perception of Peter Auriol. Arguing for the active nature of the senses in perception, Auriol applies the Scotistic doctrine of objective being to the theory of perception. Nevertheless, he still accepts some parts of the theory of species. The paper introduces Auriol's view on the mechanism of perception and his account of illusions. I argue for a direct realist reading of Auriol's theory of perception and propose that his position becomes clearer if we (...)
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  48. Péter Pázmánys Seelenlehre.Paul Richard Blum - 2013 - In Alinka Ajkay Rita Bajáki (ed.), Pázmány Nyomában. Tanulmányok Hargittay Emil tiszteletére. Mondat.
    Péter Pázmány taught philosophy at the Jesuit university of Graz, end of 16th century. This analyzes his interpretation of Aristotelian psychology.
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  49. On Peter Klein's Concept of Arbitrariness.Coos Engelsma - 2014 - Metaphilosophy 45 (2):192-200.
    According to Peter Klein, foundationalism fails because it allows a vicious form of arbitrariness. The present article critically discusses his concept of arbitrariness. It argues that the condition Klein takes to be necessary and sufficient for an epistemic item to be arbitrary is neither necessary nor sufficient. It also argues that Klein's concept of arbitrariness is not a concept of something that is obviously vicious. Even if Klein succeeds in establishing that foundationalism allows what he regards as arbitrariness, this (...)
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  50.  27
    Review of Peter Sloterdijk, 'In the Shadow of Mt. Sinai,' and Alain Badiou, 'Our Wounds Are Not So Recent'. [REVIEW]Eric D. Meyer - 2016 - Marxism and Philosophy Review of Books.
    Peter Sloterdijk's 'In the Shadow of Mt. Sinai' and Alain Badiou's 'Our Wounds Are Not So Recent' represent distinctly different attempts to come to grips with the conflict between the West (the US, the UK, France) and the Muslim world after the September 11th attacks. Although Sloterdijk finds the source of conflict in the religious zealotry of the Abrahamic religions, while Badiou blames the multinational capitalist system for drating a disaffected underclass, the two complementary perspectives work together to make (...)
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