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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547929
• 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.

数学逻辑长期以来一直在区分形式上可能和不可能方面发挥着作用，例如，哥德尔不完备性定理表明，没有足够复杂的一致形式系统可以证明数学中的简单定理可以证明其自身的一致性。近年来，模型理论家在数学中采用了建构主义方法，在“哥德尔势垒”下工作，将结构的简单属性形式化。具有理想的有限性，同时产生丰富的可定义集合。