6 found
  1.  43
    Random Closed Sets Viewed as Random Recursions.R. Daniel Mauldin & Alexander P. McLinden - 2009 - Archive for Mathematical Logic 48 (3-4):257-263.
    It is known that the box dimension of any Martin-Löf random closed set of ${\{0,1\}^\mathbb{N}}$ is ${\log_2(\frac{4}{3})}$ . Barmpalias et al. [J Logic Comput 17(6):1041–1062, 2007] gave one method of producing such random closed sets and then computed the box dimension, and posed several questions regarding other methods of construction. We outline a method using random recursive constructions for computing the Hausdorff dimension of almost every random closed set of ${\{0,1\}^\mathbb{N}}$ , and propose a general method for random closed sets (...)
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    Alexander S. Kechris. Classical Descriptive Set Theory. Graduate Texts in Mathematics, No. 156. Springer-Verlag, New York, Berlin, Heidelberg, Etc., 1995, Xviii + 402 Pp. [REVIEW]R. Daniel Mauldin - 1997 - Journal of Symbolic Logic 62 (4):1490-1491.
  3.  10
    On the Existence of Two Analytic Non-Borel Sets Which Are Not Isomorphic.A. Maitra, C. Ryll-Nardzewski, R. Daniel Mauldin, Karel Hrbacek & Stephen G. Simpson - 1984 - Journal of Symbolic Logic 49 (2):665-668.
  4.  28
    Survey of the Steinhaus Tiling Problem.Steve Jackson & R. Daniel Mauldin - 2003 - Bulletin of Symbolic Logic 9 (3):335-361.
    We survey some results and problems arising from a classic problem of Steinhaus: Is there a subset S of R 2 such that each isometric copy of mathbbZ 2 (the lattice points in the plane) meets S in exactly one point.
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    Review: Alexander S. Kechris, Classical Descriptive Set Theory. [REVIEW]R. Daniel Mauldin - 1997 - Journal of Symbolic Logic 62 (4):1490-1491.
  6.  6
    Nonuniformization Results for the Projective Hierarchy.Steve Jackson & R. Daniel Mauldin - 1991 - Journal of Symbolic Logic 56 (2):742-748.
    Let X and Y be uncountable Polish spaces. We show in ZF that there is a coanalytic subset P of X × Y with countable sections which cannot be expressed as the union of countably many partial coanalytic, or even PCA = Σ 1 2 , graphs. If X = Y = ω ω , P may be taken to be Π 1 1 . Assuming stronger set theoretic axioms, we identify the least pointclass such that any such coanalytic P (...)
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