Works by Gerdes, Peter (exact spelling)

4 found
Order:
  1.  95
    Computably enumerable equivalence relations.Su Gao & Peter Gerdes - 2001 - Studia Logica 67 (1):27-59.
    We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  2.  23
    The degrees of bi-hyperhyperimmune sets.Uri Andrews, Peter Gerdes & Joseph S. Miller - 2014 - Annals of Pure and Applied Logic 165 (3):803-811.
    We study the degrees of bi-hyperhyperimmune sets. Our main result characterizes these degrees as those that compute a function that is not dominated by any ∆02 function, and equivalently, those that compute a weak 2-generic. These characterizations imply that the collection of bi-hhi Turing degrees is closed upwards.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  23
    ${\Cal d}$-maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  4.  22
    -Maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
    Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark