O-minimality and dynamical systems

O-极小性和动力系统

• 批准号: 261961-2013
• 负责人: Speissegger, Patrick
• 金额: $ 2.48万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594686
• 关键词: minimality; dynamical; systems

Mathematical logic has long played a role in delineating between what is formally possible and impossible. For example, Gödel's incompleteness theorem shows that no consistent formal system sophisticated enough to prove simple theorems in mathematics can demonstrate its own consistency. This type of result places a limit on the scope of what is formally knowable in mathematics. In recent years, model theorists have taken on a constructivist approach to the use of logic inside mathematics. Working below the "Gödel barrier'', they have formalized simple properties of structures that have desirable finiteness properties and which, at the same time, give rise to a rich collection of definable sets.

长期以来，数理逻辑在划分形式上的可能性和不可能性方面发挥了重要作用。例如，哥德尔的不完备性定理表明，没有一个复杂到足以证明数学中简单定理的一致形式系统可以证明它自己的一致性。这种类型的结果限制了数学中形式上可知的范围。近年来，模型理论家已经采取了建构主义的方法来使用数学中的逻辑。在“哥德尔障碍”之下工作，他们已经形式化了结构的简单属性，这些结构具有理想的有限性属性，同时，这些属性产生了丰富的可定义集合。