26 found
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  1. Laurent Bienvenu, Adam R. Day, Noam Greenberg, Antonín Kučera, Joseph S. Miller, André Nies & Dan Turetsky (2014). Computing K-Trivial Sets by Incomplete Random Sets. Bulletin of Symbolic Logic 20 (1):80-90.
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  2. Laurent Bienvenu, Rod Downey, Noam Greenberg, André Nies & Dan Turetsky (2014). Characterizing Lowness for Demuth Randomness. Journal of Symbolic Logic 79 (2):526-560.
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  3.  7
    Noam Greenberg & André Nies (2011). Benign Cost Functions and Lowness Properties. Journal of Symbolic Logic 76 (1):289 - 312.
    We show that the class of strongly jump-traceable c.e. sets can be characterised as those which have sufficiently slow enumerations so they obey a class of well-behaved cost functions, called benign. This characterisation implies the containment of the class of strongly jump-traceable c.e. Turing degrees in a number of lowness classes, in particular the classes of the degrees which lie below incomplete random degrees, indeed all LR-hard random degrees, and all ω-c.e. random degrees. The last result implies recent results of (...)
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  4.  14
    Noam Greenberg & Joseph S. Miller (2009). Lowness for Kurtz Randomness. Journal of Symbolic Logic 74 (2):665-678.
    We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...)
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  5.  16
    Rod Downey, Noam Greenberg & Rebecca Weber (2007). Totally Ω-Computably Enumerable Degrees and Bounding Critical Triples. Journal of Mathematical Logic 7 (2):145-171.
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  6.  11
    Peter Cholak, Noam Greenberg & Joseph S. Miller (2006). Uniform Almost Everywhere Domination. 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.  17
    Chris Conidis, Noam Greenberg & Daniel Turetsky (2013). Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle. Notre Dame Journal of Formal Logic 54 (2):233-252.
    We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.
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  8.  16
    Barbara F. Csima, Rod Downey, Noam Greenberg, Denis R. Hirschfeldt & Joseph S. Miller (2006). Every 1-Generic Computes a Properly 1-Generic. Journal of Symbolic Logic 71 (4):1385 - 1393.
    A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.
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  9.  16
    Noam Greenberg & Antonio Montalbán (2003). Embedding and Coding Below a 1-Generic Degree. Notre Dame Journal of Formal Logic 44 (4):200-216.
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  10.  9
    Noam Greenberg (2011). A Random Set Which Only Computes Strongly Jump-Traceable C.E. Sets. Journal of Symbolic Logic 76 (2):700 - 718.
    We prove that there is a ${\mathrm{\Delta }}_{2}^{0}$ , 1-random set Y such that every computably enumerable set which is computable from Y is strongly jump-traceable. We also show that for every order function h there is an ω-c.e. random set Y such that every computably enumerable set which is computable from Y is h-jump-traceable. This establishes a correspondence between rates of jump-traceability and computability from ω-c.e. random sets.
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  11.  10
    Noam Greenberg, Antonio Montalbán & Richard Shore (2004). Generalized High Degrees Have the Complementation Property. Journal of Symbolic Logic 69 (4):1200-1220.
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  12.  3
    Sakae Fuchino, Noam Greenberg & Saharon Shelah (2006). Models of Real-Valued Measurability. Annals of Pure and Applied Logic 142 (1):380-397.
    Solovay’s random-real forcing [R.M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory , Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428] is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay’s model that do not follow from the existence of real-valued measurability.
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  13.  24
    Noam Greenberg (2005). The Role of True Finiteness in the Admissible Recursively Enumerable Degrees. Bulletin of Symbolic Logic 11 (3):398-410.
    We show, however, that this is not always the case.
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  14.  4
    Noam Greenberg, Richard A. Shore & Theodore A. Slaman (2006). The Theory of the Metarecursively Enumerable Degrees. Journal of Mathematical Logic 6 (01):49-68.
  15.  3
    Mark Colyvan Burgess, Anuj Dawar, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier (2010). College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 16 (3).
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  16.  5
    Noam Greenberg & Saharon Shelah (2014). Models of Cohen Measurability. Annals of Pure and Applied Logic 165 (10):1557-1576.
    We show that in contrast with the Cohen version of Solovay's model, it is consistent for the continuum to be Cohen-measurable and for every function to be continuous on a non-meagre set.
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  17.  2
    Anuj Dawar Colyvan, Noam Greenberg, Rahim Moosa, Ernest Schimmerling & Alex Simp (2012). Ny 12604, Usa. Bulletin of Symbolic Logic 18 (4).
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  18.  3
    Mark Colyvan Burgess, Anuj Dawar, Marcelo Fiore, Noam Greenberg & Hannes Leitgeb (2010). The Association for Symbolic Logic Publishes Analytical Reviews of Selected Books and Articles in the Field of Symbolic Logic. The Reviews Were Published in The Journal of Symbolic Logic From the Founding of the Journal in 1936 Until the End of 1999. The Association Moved the Reviews to This Bulletin, Beginning in 2000. The Reviews Section is Edited by Steve Awodey (Managing Editor), John Baldwin, John. [REVIEW] Bulletin of Symbolic Logic 16 (1).
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  19.  3
    Anuj Dawar Colyvan, Marcelo Fiore, Noam Greenberg, Hannes Leitgeb, Rahim Moosa, Ernest Schimmerling, Carsten Schürmann & Kai Wehmeier (2011). College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 17 (1).
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  20.  5
    Noam Greenberg, Antonio Montalbán & Theodore A. Slaman (2013). Relative to Any Non-Hyperarithmetic Set. Journal of Mathematical Logic 13 (1):1250007.
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  21.  2
    Verónica Becher, C. T. Chong, Rod Downey, Noam Greenberg, Antonin Kucera, Bjørn Kjos-Hanssen, Steffen Lempp, Antonio Montalbán, Jan Reimann & Stephen Simpson (2008). Conference on Computability, Complexity and Randomness. Bulletin of Symbolic Logic 14 (4):548-549.
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  22.  2
    Michael Benedikt, Andreas Blass, Natasha Dobrinen, Noam Greenberg, Denis R. Hirschfeldt, Salma Kuhlmann, Hannes Leitgeb, William J. Mitchell & Thomas Wilke (2007). Gainesville, Florida March 10–13, 2007. Bulletin of Symbolic Logic 13 (3).
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  23. Rod Downey, Noam Greenberg & Joseph S. Miller (2008). The Upward Closure of a Perfect Thin Class. Annals of Pure and Applied Logic 156 (1):51-58.
    There is a perfect thin class whose upward closure in the Turing degrees has full measure . Thus, in the Muchnik lattice of classes, the degree of 2-random reals is comparable with the degree of some perfect thin class. This solves a question of Simpson [S. Simpson, Mass problems and randomness, Bulletin of Symbolic Logic 11 1–27].
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  24. Johanna N. Y. Franklin, Noam Greenberg, Frank Stephan & Guohua Wu (2013). Anti-Complex Sets and Reducibilities with Tiny Use. Journal of Symbolic Logic 78 (4):1307-1327.
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  25. Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky (2015). Computability and Uncountable Linear Orders I: Computable Categoricity. Journal of Symbolic Logic 80 (1):116-144.
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  26. Noam Greenberg, Asher M. Kach, Steffen Lempp & Daniel D. Turetsky (2015). Computability and Uncountable Linear Orders II: Degree Spectra. Journal of Symbolic Logic 80 (1):145-178.
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