10 found
Order:
Disambiguations
Geoffrey Laforte [9]Geoffrey L. Laforte [2]
  1.  20
    On Schnorr and Computable Randomness, Martingales, and Machines.Rod Downey, Evan Griffiths & Geoffrey Laforte - 2004 - Mathematical Logic Quarterly 50 (6):613-627.
    We examine the randomness and triviality of reals using notions arising from martingales and prefix-free machines.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  2.  21
    The Isolated D. R. E. Degrees Are Dense in the R. E. Degrees.Geoffrey Laforte - 1996 - Mathematical Logic Quarterly 42 (1):83-103.
    In the present paper we prove that the isolated differences of r. e. degrees are dense in the r. e. degrees.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  3. Decomposition and Infima in the Computably Enumerable Degrees.Rodney G. Downey, Geoffrey L. Laforte & Richard A. Shore - 2003 - Journal of Symbolic Logic 68 (2):551-579.
    Given two incomparable c.e. Turing degrees a and b, we show that there exists a c.e. degree c such that c = (a ⋃ c) ⋂ (b ⋃ c), a ⋃ c | b ⋃ c, and c < a ⋃ b.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4. Why Godel's Theorem Cannot Refute Computationalism: A Reply to Penrose.Geoffrey Laforte, Pat Hayes & Kenneth M. Ford - 1998 - Artificial Intelligence 104.
  5.  10
    Equivalence Structures and Isomorphisms in the Difference Hierarchy.Douglas Cenzer, Geoffrey LaForte & Jeffrey Remmel - 2009 - Journal of Symbolic Logic 74 (2):535-556.
    We examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak ω-c.e. categoricity, and that $\Delta _2^0 $ -categoricity is equivalent to our notion of graph-ω-c.e. categoricity.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  12
    Relative Enumerability in the Difference Hierarchy.Marat M. Arslanov, Geoffrey L. Laforte & Theodore A. Slaman - 1998 - Journal of Symbolic Logic 63 (2):411-420.
    We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  7.  9
    Isolation in the CEA Hierarchy.Geoffrey LaForte - 2004 - Archive for Mathematical Logic 44 (2):227-244.
    Examining various kinds of isolation phenomena in the Turing degrees, I show that there are, for every n>0, (n+1)-c.e. sets isolated in the n-CEA degrees by n-c.e. sets below them. For n≥1 such phenomena arise below any computably enumerable degree, and conjecture that this result holds densely in the c.e. degrees as well. Surprisingly, such isolation pairs also exist where the top set has high degree and the isolating set is low, although the complete situation for jump classes remains unknown.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  18
    A Δ02 Set with Barely Σ02 Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700 - 1718.
    We construct a Δ 0 2 degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9.  3
    A $Delta^02$ Set with Barely $Sigma^02$ Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700-1718.
    We construct a $\Delta^0_2$ degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10.  2
    A Set with Barely Degree.Rod Downey, Geoffrey Laforte & Steffen Lempp - 1999 - Journal of Symbolic Logic 64 (4):1700-1718.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark