9 found
Order:
  1.  5
    Open Sets Satisfying Systems of Congruences.Randall Dougherty - 2001 - Journal of Mathematical Logic 1 (2):247-303.
    A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the Banach–Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2.  4
    Solutions to Congruences Using Sets with the Property of Baire.Randall Dougherty - 2001 - Journal of Mathematical Logic 1 (2):221-245.
    Hausdorff's paradoxical decomposition of a sphere with countably many points removed actually produced a partition of this set into three pieces A,B,C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C. While refining the Banach–Tarski paradox, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences: the only nontrivial restriction is that the system should not require (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  3.  12
    Monotone but Not Positive Subsets of the Cantor Space.Randall Dougherty - 1987 - Journal of Symbolic Logic 52 (3):817-818.
  4.  4
    Critical Points in an Algebra of Elementary Embeddings.Randall Dougherty - 1993 - Annals of Pure and Applied Logic 65 (3):211-241.
    Dougherty, R., Critical points in an algebra of elementary embeddings, Annals of Pure and Applied Logic 65 211-241.Given two elementary embeddings from the collection of sets of rank less than λ to itself, one can combine them to obtain another such embedding in two ways: by composition, and by applying one to the other. Hence, a single such nontrivial embedding j generates an algebra of embeddings via these two operations, which satisfies certain laws . Laver has shown, among other things, (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  3
    The Complexity of Antidifferentiation.Randall Dougherty, Alexander S. Kechris, Ferenc Beleznay & Matthew Foreman - 2001 - Bulletin of Symbolic Logic 7 (3):385-388.
  6.  17
    Banach-Tarski Paradox Using Pieces with the Property of Baire.Randall Dougherty & Matthew Foreman - 2001 - Bulletin of Symbolic Logic 7 (4):537-538.
  7.  14
    Narrow Coverings of Ω-Ary Product Spaces.Randall Dougherty - 1997 - Annals of Pure and Applied Logic 88 (1):47-91.
    Results of Sierpiski and others have shown that certain finite-dimensional product sets can be written as unions of subsets, each of which is ‘narrow’ in a corresponding direction; that is, each line in that direction intersects the subset in a small set. For example, if the set ω × ω is partitioned into two pieces along the diagonal, then one piece meets every horizontal line in a finite set, and the other piece meets each vertical line in a finite set. (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  8.  24
    Canonical Universes and Intuitions About Probabilities.Randall Dougherty & Jan Mycielski - 2006 - Dialectica 60 (4):357–368.
  9.  4
    Sequential Discreteness and Clopen-I-Boolean Classes.Randall Dougherty - 1987 - Journal of Symbolic Logic 52 (1):232-242.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark