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Nonbounding 𝑛-C.E. 𝑄-Degrees

  • Roland Omanadze
Published/Copyright: March 11, 2010
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Georgian Mathematical Journal
From the journal Volume 16 Issue 4

Abstract

We prove that for any noncomputable c.e. set 𝐴 there is a non-computable c.e. set 𝐡 βŠ† 𝐴 such that for every noncomputable c.e. set π‘Š we have π‘Š β‰°βƒ₯ 𝑄𝐴 – 𝐡 < 𝑄𝐴. We show that if c.e. 𝑄-degrees 𝐚 and 𝐛 form a minimal pair in the c.e. 𝑄-degrees, then 𝐚 and 𝐛 form a minimal pair in the 𝑄-degrees.

Key words and phrases:: 𝑄-degree; 𝑛-c.e. sets; minimal pair
Received: 2008-11-24
Revised: 2009-08-12
Published Online: 2010-03-11
Published in Print: 2009-December

Β© Heldermann Verlag

Articles in the same Issue

  1. On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
  2. Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
  3. Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
  4. A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
  5. The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
  6. Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
  7. On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their BΓ©zier Variant
  8. On Nonmeasurable Functions of Two Variables and Iterated Integrals
  9. Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
  10. On Functional Equations Connected with Quadrature Rules
  11. The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
  12. A Counterexample on Embedding of Spaces
  13. On Solutions of a Singular Viscoelastic Equation with an Integral Condition
  14. Nonbounding 𝑛-C.E. 𝑄-Degrees
  15. Nonequivalence of Unilateral Strong Differentiation Bases in
https://doi.org/10.1515/GMJ.2009.779
Keywords for this article
𝑄-degree; 𝑛-c.e. sets; minimal pair

Articles in the same Issue

  1. On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
  2. Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
  3. Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
  4. A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
  5. The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
  6. Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
  7. On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their BΓ©zier Variant
  8. On Nonmeasurable Functions of Two Variables and Iterated Integrals
  9. Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
  10. On Functional Equations Connected with Quadrature Rules
  11. The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
  12. A Counterexample on Embedding of Spaces
  13. On Solutions of a Singular Viscoelastic Equation with an Integral Condition
  14. Nonbounding 𝑛-C.E. 𝑄-Degrees
  15. Nonequivalence of Unilateral Strong Differentiation Bases in
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