Title：On Formal Foundation of Meta-Mathematics
Speaker：Qi Feng （BIMSA）
Abstract：Ever since 1879 when Frege published Begriffsschrift, the study of logic and the study of foundations of mathematics became parts of mathematics. Actually, such studies are parts of metamathematics. Generally, within the field of meta-mathematics, all studies or investigations, such as Was sind und was sollen die Zahlen? (Dedekind,1888), The principles of Arithmetic (Peano, 1889), Basic Laws of Arithmetic (Frege, 1893), Principia Mathematica (Whitehead and Russell, 1910-1913), Grundzüge der theoretischen Logik (Hilbert and Ackerman, 1928), G ö del’s works on Completeness of first-order predicate logic and Incompleteness of Peano arithmetic (1929, 1931), Tarski’s work on the concept of truth in formalized languages (1929-1935), etc., are carried out in informal and intuitive ways in the meta-theory parts, although the objective theories are well-formalized. Naturally, there arises the question whether such studies could possibly be based on a formalized meta-theory in such a way that the meta-theory would be expressed in a formal language, deductions would be carried out formally by applications of explicitly stated formal rules and entirely based on a specific set of fundamental formal principles (starting with a specifically finitary formal part), not by conviction, not based on the intuitive concept of natural numbers and intuitive mathematical induction, not by intuitive inferences, not by appealing to the meaning and evidence. In this talk, I would like to report my efforts in the past few years attempting to answer this question affirmatively. Namely, I would like to present a pure formal meta-theory CFZFC, starting from a specifically finitary formal language and a specifically finitary set of principles and rules, developed entirely by pure formal inferences, which will be sufficient for the development of meta-mathematics and most part of mathematics.
Time：5.22（Friday），14:00-15:00
Venue：Gewu Building 315
About the Speaker：冯琦，北京雁栖湖应用数学研究院研究员，研究方向为数理逻辑、公理化集合论及无穷组合理论。在实数集正则性领域与Magidor、Woodin合作完成奠基性工作，与Jensen合作构建复杂内模型理论，在大基数与印证原理研究中取得系列突破，并与Woodin合作推进连续统假设研究。出版《数理逻辑导引》、《集合论导引》、《元数学基础》等教材。曾任国际符号逻辑协会东亚分会理事长及理事、中国科学院数学研究所副所长。1977年考入哈尔滨工业大学计算机科学系，1988年获宾州州立大学博士学位。1990年赴新加坡国立大学任讲师，1998年任中科院数学所研究员。2004-2007年执教清华大学数学系，期间参与数学院-新加坡国立大学-加州伯克利分校联合培养项目，曾担任德国柏林洪堡大学Mer Cator客座教授。2000年获国家杰出青年科学基金，2003年入选中科院百人计划，2017年获北京市教学名师奖。
