Topic: |
Applied Logics Seminar Series(XL) -- Categoricity spectra and effective classifications |

Speaker: |
Prof. Nikolay Bazhenov (Sobolev Institute of Mathematics, Russia ) |

Date: |
2018-10-12 (Fri) 15:30 – 17:30 |

Location: |
Auditorium 106 at IIS new Building |

Host: |
Churn-Jung Liau |

**Abstract:**
The general area of effective algebra is devoted to studying the algorithmic content of mathematical structures. The standard model for such investigations is a (Turing) computable presentation of an algebraic structure. A computable structure S is computably categorical if for any computable presentation A of S, there is a Turing computable isomorphism from A onto S. The notion of categoricity spectrum, which is built upon computable categoricity, captures the complexity of isomorphisms between different computable presentations of a given structure. For a class of structures K, effective classification gives a measure of complexity for computably presentable members of K. In the talk, we give a review of recent results on categoricity spectra and related effective classification problems.