主 题: Introduction to Model Theory
报告人: Cori Joseph, René (Université Paris Diderot, Institut de Mathématiques de Jussieu Paris Rive Gauche)
时 间: 2017-05-02 15:00-17:00
地 点: 数学中心 甲乙丙楼1层 82J04教室
课程时间：2017年5月2日-2017年6月13日
具体时间见链接：http://bicmr.pku.edu.cn/content/show/70-1809.html
Abstract: This course will be given in May and June 2017 at Peking University, Beijing. Its aim is to present the main tools and the basic results in Model Theory. It is recommended to students interested in Mathematical Logic and particularly to those who wish to attend Zoé Chatzidakis lectures on Model theory of valued fields and applications. No specific knowledge in Logic is required, but we expect some familiarity with elementary Mathematics: naive set theory, standard algebraic structures, linear algebra, and elementary analysis. Thus the course is suitable for third or fourth year undergraduate students.
In the first part of the course we will introduce the basic notions of first order Logic: languages, formulas, theories, structures and models; morphisms, submodels, elementary equivalence, elementary extensions, ultra-products, complete theories; inference rules. We will prove the main theorems: compactness, completeness, Lowenheim-Skolem, Los … We will need some notions from axiomatic set theory, mainly ordinal and cardinal numbers.If we have enough time, we will give a general presentation of set theory. Otherwise we will just give the needed results.
The second part of the course will be devoted to some further topics in Model Theory, chosen among the following: diagrams, interpolation and definability theorems, Fraissé's back and forth method, quantfier elimination, preservation theorems, categoricity, saturated models, omitting types theorem. We shall give many examples of theories and structures: groups, rings, fields, ordered structures, Peano arithmetic…
May 2 15:00–17:00
May 3 10:00—12:00
May 4 8:00—10:00
May 5 10:00—13:00
May 9 15:00–17:00
May 10 10:00—12:00
May 11 8:00—10:00
May 12 10:00—13:00
May 16 15:00–17:00
May 17 10:00—12:00
May 18 8:00—10:00
May 19 10:00—13:00
May 23 15:00–17:00
May 25 8:00—10:00
May 26 13:00—15:00
June 1 8:00—10:00
June 2 13:00—15:00
June 6 15:00–17:00
June 8 8:00—10:00
June 9 13:00—15:00
June 13 15:00–17:00
