Switch to: Citations

Add references

You must login to add references.
  1. A Construction for Recursive Linear Orderings.C. J. Ash - 1991 - Journal of Symbolic Logic 56 (2):673-683.
    We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Computable Structures and the Hyperarithmetical Hierarchy.C. J. Ash - 2000 - Elsevier.
    This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...)
    Direct download  
     
    Export citation  
     
    Bookmark   37 citations  
  • Degree Spectra and Computable Dimensions in Algebraic Structures.Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko - 2002 - Annals of Pure and Applied Logic 115 (1-3):71-113.
    Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   39 citations  
  • Degree Spectra of Relations on Computable Structures.Denis R. Hirschfeldt - 2000 - Bulletin of Symbolic Logic 6 (2):197-212.
    There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. Several different notions of effectiveness of model-theoretic structures have been investigated. This communication is concerned withcomputablestructures, that is, structures with computable domains whose constants, functions, and relations are uniformly computable.In model theory, we identify isomorphic structures. (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • The -Spectrum of a Linear Order.Russell Miller - 2001 - Journal of Symbolic Logic 66 (2):470-486.
    Slaman and Wehner have constructed structures which distinguish the computable Turing degree 0 from the noncomputable degrees, in the sense that the spectrum of each structure consists precisely of the noncomputable degrees. Downey has asked if this can be done for an ordinary type of structure such as a linear order. We show that there exists a linear order whose spectrum includes every noncomputable Δ 0 2 degree, but not 0. Since our argument requires the technique of permitting below a (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • On Computable Self-Embeddings of Computable Linear Orderings.Rodney G. Downey, Bart Kastermans & Steffen Lempp - 2009 - Journal of Symbolic Logic 74 (4):1352 - 1366.
    We solve a longstanding question of Rosenstein, and make progress toward solving a longstanding open problem in the area of computable linear orderings by showing that every computable ƞ-like linear ordering without an infinite strongly ƞ-like interval has a computable copy without nontrivial computable self-embedding. The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
  • Degrees of Orderings Not Isomorphic to Recursive Linear Orderings.Carl G. Jockusch & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 52 (1-2):39-64.
    It is shown that for every nonzero r.e. degree c there is a linear ordering of degree c which is not isomorphic to any recursive linear ordering. It follows that there is a linear ordering of low degree which is not isomorphic to any recursive linear ordering. It is shown further that there is a linear ordering L such that L is not isomorphic to any recursive linear ordering, and L together with its ‘infinitely far apart’ relation is of low (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  • Some Effects of Ash–Nerode and Other Decidability Conditions on Degree Spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 55 (1):51-65.
    With every new recursive relation R on a recursive model , we consider the images of R under all isomorphisms from to other recursive models. We call the set of Turing degrees of these images the degree spectrum of R on , and say that R is intrinsically r.e. if all the images are r.e. C. Ash and A. Nerode introduce an extra decidability condition on , expressed in terms of R. Assuming this decidability condition, they prove that R is (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  • Uncountable Degree Spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 54 (3):255-263.
    We consider a recursive model and an additional recursive relation R on its domain, such that there are uncountably many different images of R under isomorphisms from to some recursive model isomorphic to . We study properties of the set of Turing degrees of all these isomorphic images of R on the domain of.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • The Possible Turing Degree of the Nonzero Member in a Two Element Degree Spectrum.Valentina S. Harizanov - 1993 - Annals of Pure and Applied Logic 60 (1):1-30.
    We construct a recursive model , a recursive subset R of its domain, and a Turing degree x 0 satisfying the following condition. The nonrecursive images of R under all isomorphisms from to other recursive models are of Turing degree x and cannot be recursively enumerable.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  • Every Recursive Boolean Algebra is Isomorphic to One with Incomplete Atoms.Rod Downey - 1993 - Annals of Pure and Applied Logic 60 (3):193-206.
    The theorem of the title is proven, solving an old question of Remmel. The method of proof uses an algebraic technique of Remmel-Vaught combined with a complex tree of strategies argument where the true path is needed to figure out the final isomorphism.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Degree Spectra of the Successor Relation of Computable Linear Orderings.Jennifer Chubb, Andrey Frolov & Valentina Harizanov - 2009 - Archive for Mathematical Logic 48 (1):7-13.
    We establish that for every computably enumerable (c.e.) Turing degree b the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Relations Intrinsically Recursive in Linear Orders.Michael Moses - 1986 - Mathematical Logic Quarterly 32 (25‐30):467-472.
  • Relations Intrinsically Recursive in Linear Orders.Michael Moses - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (25-30):467-472.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations