1,127 research outputs found

    Characterizing the strongly jump-traceable sets via randomness

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    AbstractWe show that if a set A is computable from every superlow 1-random set, then A is strongly jump-traceable. Together with a result of Greenberg and Nies [Noam Greenberg, André Nies, Benign cost functions and lowness properties, J. Symbolic Logic 76 (1) (2011) 289–312], this theorem shows that the computably enumerable (c.e.) strongly jump-traceable sets are exactly the c.e. sets computable from every superlow 1-random set.We also prove the analogous result for superhighness: a c.e. set is strongly jump-traceable if and only if it is computable from every superhigh 1-random set.Finally, we show that for each cost function c with the limit condition there is a 1-random Δ20 set Y such that every c.e. set A⩽TY obeys c. To do so, we connect cost function strength and the strength of randomness notions. Together with a theorem of Greenberg and Nies (ibd.), this result gives a full correspondence between obedience of cost functions and being computable from Δ201-random sets

    Maximality in the ⍺-C.A. Degrees

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    In [4], Downey and Greenberg define the notion of totally ⍺-c.a. for appropriately small ordinals ⍺, and discuss the hierarchy this notion begets on the Turing degrees. The hierarchy is of particular interest because it has already given rise to several natural definability results, and provides a definable antichain in the c.e. degrees. Following on from the work of [4], we solve problems which are left open in the aforementioned relating to this hierarchy. Our proofs are all constructive, using strategy trees to build c.e. sets, usually with some form of permitting. We identify levels of the hierarchy where there is absolutely no collapse above any totally ⍺-c.a. c.e. degree, and construct, for every ⍺ ≼ ε0, both a totally ⍺-c.a. c.e. minimal cover and a chain of totally ⍺-c.a. c.e. degrees cofinal in the totally ⍺-c.a. c.e. degrees in the cone above the chain's least member

    Michael Greenberg speaks at WCSU

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    Author Michael Greenberg speaks at Western Connecticut State University on October 9, 2009

    Michael Greenberg Speaks at WCSU

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    Author Michael Greenberg speaks to a small group during the day on October 28, 2009.</p

    ABOUT MIKHAIL S. GREENBERG

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    The introductory article of the issue – the obituary – is devoted to the outstanding Soviet and Russian lawyer – professor Mikhail S. Greenberg. The author dwells on the main mile-stones of M.S. Greenberg's scientific biography: from studying at Leningrad State University to conferring the title "Honoured Lawyer of the Russian Federation" during his work in Omsk State University, highlights the main provisions of his scientific works, characterizes the personal qualities of M.S. Greenberg

    Michael Greenberg speaks at WCSU

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    Author Michael Greenberg talks about his book, Hurry Down Sunshine, at Western Connecticut State University on October 28, 2009

    Michael Greenberg Speaks at WCSU

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    Author Michael Greenberg speaks to a small group on the afternoon of October 28, 2009 at WestConn

    Český Greenberg? Mukařovský a estetický formalismus

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    [A Czech Greenberg? Mukařovský and Aesthetic Formalism] This article revisits Tomáš Pospiszyl’s discussion of the split between the North American and the Czechoslovak postwar modernism as a difference between the views of two critics who dominated the American and the Czechoslovak art scene, respectively--Clement Greenberg and Jindřich Chalupecký. Pospiszyl convincingly traces the evolution of American art to what has been called Greenberg’s “formalism,” and the developments on the Czechoslovak scene to Chalupecký’s ideas about art as part of social social interactions. Though the author of the article agrees with this analysis of Czechoslovak modernism as anti-formalist, he seeks to draw attention to the writings of the Czech literary theorist Jan Mukařovský, which were contemporaneous with Chalupecký’s and Greenberg’s--in particular Mukařovský’s 1944 lecture “The Essence of the Visual Arts.” The author provides a comparative analysis of Mukařovský and Greenberg, suggesting that the former was quite close to the latter’s “formalism.” This might seem incorrect, given that Mukařovský is considered to be a precursor of the semiotic theory of art, which is generally understood as antithetical to formalism. The solution, he argues, is to realize that Greenberg is subtler, hence not so "formalist” after all. At any rate, it turns out that in addition to Chalupecký’s “social” theory of art, Mukařovský had a more “formalist” alternative which – for well-known historical reasons – had no effect on the subsequent development of Czechoslovak modernism

    Cannibals and Catholics: Reading the Reading of Evelyn Waugh\u27s Black Mischief

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    Jonathan Greenberg (Montclair State University) explores satire\u27s unstable dynamic of enjoyment and identification, one always threatening to careen out of the author\u27s control. As an example of this instability, Greenberg offers the messy public debate in which Waugh attempted to defend himself from the Catholic press\u27s charge that his novel “Black Mischief” was an immoral book, and Greenberg uses this debate as a point of departure to explore satire\u27s dialectical nature: the structural inextricability of morality and sadistic pleasure, outrage and amusement, anger and blasé indifference
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