Computability and Effective Constructions in Mathematics

数学中的可计算性和有效构造

• 批准号: 0075899
• 负责人: Steffen Lempp
• 金额: $ 3.52万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0075899&HistoricalAwards=false
• 关键词: Computability; Effective; Constructions; Mathematics

PROJECT SUMMARYThe purpose of this award is to provide travel support to allow Douglas Cenzer (University of Florida), Valentina Harizanov (George Washington University), Julia Knight (University of Notre Dame), Steffen Lempp and Reed Solomon (University of Wisconsin-Madison), and Andre Nies (University of Chicago) as well as Marat Arslanov (Kazan State University), Sergey Goncharov and Andrei Morozov (Russian Academy of Sciences, Novosibirsk), and Serikzhan Badaev and Mikhail Peretyat'kin (Kazakh Academy of Sciences, Almaty) to make one research visit each to work collaboratively with their counterparts in the other country, as well as a total of three additional trips by students.The focus of the proposed cooperative research is the theory of computability and its applications to other areas, in particular algebra and model theory. Specific research topics include the study of computable approximations to sets, the complexity of presentations of algebraic structures, the complexity of additional relations on effective structures, the complexity of isomorphisms of effective structures, numerations of algebraic structures, automorphism groups of computable structures, and applications to abelian $p$-groups, to groups of computable permutations, and to Boolean algebras

项目摘要该奖项的目的是提供旅行支持，以允许道格拉斯·塞泽（佛罗里达大学），瓦伦蒂娜·哈扎那诺夫（​​乔治华盛顿大学），朱莉娅·奈特（朱莉娅·奈特（Notre Dame）），史蒂芬·莱姆普（Steffen Lempp）和里德·所罗门（Reed Solomon）以及安德烈·尼斯（Andre Nies）（芝加哥大学）以及马拉特·阿尔斯拉诺夫（Kazan State University），Sergey Goncharov和Andrei Morozov（俄罗斯科学学院，Novosibirsk），Serikzhan Badaev和Mikhail Peretyat'kin（Kazakh of Sciences of Sciences of Science，Almaty）为了让每一次研究访问与另一个国家的同行一起合作，以及学生共有三次旅行。拟议的合作研究的重点是计算性理论及其在其他领域的应用理论，尤其是其应用于其他领域代数和模型理论。具体的研究主题包括研究集合的可计算近似值，代数结构的表现的复杂性，有效结构的额外关系的复杂性，有效结构的同构复杂性，代数结构的数字，可计算结构的自动化组的数字以及应用结构的自动化和应用。到Abelian $ p $ - 群体，可计算排列的组和布尔代数