### Abstract

Original language | English |
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Title of host publication | Lecture Notes in Computer Science |

Subtitle of host publication | TAMC 2019 : Theory and Applications of Models of Computation |

Publisher | Springer |

Pages | 1 |

Number of pages | 13 |

Volume | 11436 |

Publication status | Published - Apr 13 2019 |

### Publication series

Name | Lecture Notes in Computer Science |
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### Cite this

*Lecture Notes in Computer Science: TAMC 2019 : Theory and Applications of Models of Computation*(Vol. 11436 , pp. 1). (Lecture Notes in Computer Science). Springer.

**Computable Isomorphisms of Distributive Lattices.** / Bazhenov, Nikolay; Mustafa, Manat; Yamaleev, Mars.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science: TAMC 2019 : Theory and Applications of Models of Computation.*vol. 11436 , Lecture Notes in Computer Science, Springer, pp. 1.

}

TY - GEN

T1 - Computable Isomorphisms of Distributive Lattices

AU - Bazhenov, Nikolay

AU - Mustafa, Manat

AU - Yamaleev, Mars

PY - 2019/4/13

Y1 - 2019/4/13

N2 - A standard tool for the classifying computability-theoretic complexity of equivalence relations is provided by computable reducibility. This gives rise to a rich degree-structure which has been extensively studied in the literature. In this paper, we show that equivalence relations, which are complete for computable reducibility in various levels of the hyperarithmetical hierarchy, arise in a natural way in computable structure theory. We prove that for any computable successor ordinal $\alpha$, the relation of $\Delta^0_{\alpha}$ isomorphism for computable distributive lattices is $\Sigma^0_{\alpha+2}$ complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.

AB - A standard tool for the classifying computability-theoretic complexity of equivalence relations is provided by computable reducibility. This gives rise to a rich degree-structure which has been extensively studied in the literature. In this paper, we show that equivalence relations, which are complete for computable reducibility in various levels of the hyperarithmetical hierarchy, arise in a natural way in computable structure theory. We prove that for any computable successor ordinal $\alpha$, the relation of $\Delta^0_{\alpha}$ isomorphism for computable distributive lattices is $\Sigma^0_{\alpha+2}$ complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.

M3 - Conference contribution

VL - 11436

T3 - Lecture Notes in Computer Science

SP - 1

BT - Lecture Notes in Computer Science

PB - Springer

ER -