$\Sigma^0_1$ and $\Pi^0_1$ Equivalence Structures

  • Authors:

  • Douglas Cenzer;Valentina Harizanov;Jeffrey B. Remmel

  • Affiliations:

  • Department of Mathematics, University of Florida, Gainesville 32611;Department of Mathematics, George Washington University, Washington 20052;Department of Mathematics, University of California-San Diego, La Jolla 92093

  • Venue:
  • CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

We study computability theoretic properties of $\Sigma _{1}^{0}$ and $\Pi _{1}^{0}$ equivalence structures and how they differ from computable equivalence structures or equivalence structures that belong to the Ershov difference hierarchy. Our investigation includes the complexity of isomorphisms between $\Sigma _{1}^{0}$ equivalence structures and between $\Pi _{1}^{0}$ equivalence structures.