講 題： |
應用邏輯討論會系列 (XL) - Categoricity spectra and effective classifications |

講 者： |
Nikolay Bazhenov 教授 (俄羅斯科學院西伯利亞分院, 索博列夫數學研究所) |

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

地 點： |
資訊所新館106演講廳 |

邀請人： |
廖純中 |

**摘要:**
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.