The Model Theory of Valued Fields with Analytic Structure

解析结构的值域模型论

基本信息

  • 批准号:
    0070724
  • 负责人:
  • 金额:
    $ 17.55万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2000
  • 资助国家:
    美国
  • 起止时间:
    2000-06-01 至 2004-05-31
  • 项目状态:
    已结题

项目摘要

Lipshitz and Robinson propose to continue their collaborative investigationinto the model theory of valued fields with analytic structure. Classical rigid analytic geometry is based on rings of strictly convergent power series,i.e., power series convergent on products of "closed" discs. The proposers have introduced new rings of power series convergent on products of "closed" and "open" discs. These rings of separated power series share many of the desirable algebraic properties of the smaller rings of strictly convergent power series. In addition they are particularly well suited for model theoretic applications. Lipshitz and Robinson propose to continue to develop the commutative algebra of rings of separated power series and the corresponding rigid geometry in analogy to the classical case. On the model theory side they propose to broaden their investigation to consider the model theory of non-algebraically-closed valued fields with analytic structure and also to consider questions of uniformity over different fields in the theory of rigid subanalytic sets. The methods to be employed come from model theory, commutative algebra and algebraic geometry.The sets of points in Euclidean space over the field of real numbers definedby systems of equations and inequalities among analytic functions are calledsemi-analytic sets. This class of sets is basic to analytic geometry. Theprojection (i.e. the shadow) of a semi-analytic set on a lower dimensionalsubspace is called subanalytic. There are more subanalytic sets than semi-analytic sets, and their behavior is more complicated. There is a natural interest in subanalytic sets. These are exactly the sets that can bemathematically defined from the semi-analytic sets, in the sense of formallogic. Furthermore, real subanalytic sets arise in several branches ofmathematics such as differential equations and geometry. Similar classes of sets arise naturally, for example in number theory, over fields different from the real numbers, where the notion of distance has rather different properties. Such fields are called non-Archimedean. The corresponding subanalytic sets, however, share many of the nice properties of their real cousins. Lipshitz and Robinson will continue their investigation of the properties of these non-Archimedean subanalytic sets, using methods from mathematical logic, commutative algebra andalgebraic geometry. Having developed key elements of theory in the Non-Archimedean case, they propose to apply their ideas to extend the classes of fields to whichthese results apply. In particular, they plan to apply ideas developed inthe non-Archimedean setting to the real case, thereby enlarging the class ofreal sets whose nice geometric properties can be established by these means.Since many of the procedures used to extract geometric information aboutthese sets do not vary from field to field, the also plan a careful study of thenature of this uniformity.
Lipshitz和罗宾逊建议继续他们的合作研究,研究具有解析结构的值域的模型理论。 经典的刚性解析几何是基于严格收敛的幂级数环,即,幂级数收敛于“闭”圆盘的乘积。提出者引入了收敛于“闭”和“开”圆盘的乘积的幂级数的新环。 这些环的分离幂级数共享许多理想的代数性质的较小的环严格收敛的幂级数。 此外,它们特别适合模型理论应用。Lipshitz和罗宾逊建议继续发展交换代数环的分离幂级数和相应的刚性几何类似的经典情况。 在模型理论方面,他们建议扩大他们的调查,以考虑模型理论的非代数闭值领域的分析结构,并考虑问题的一致性在不同领域的理论刚性subanalytic集。 所用的方法来自模型论、交换代数和代数几何,由解析函数间的方程组和不等式所定义的真实的数域上的欧氏空间中的点集称为半解析集。这类集合是解析几何的基础。半解析集在低维子空间上的投影(即阴影)称为次解析集。亚解析集比半解析集多,其行为也更复杂。有一个自然的兴趣在subanalytic集。在形式逻辑的意义上,这些正是可以从半解析集合中数学定义的集合。此外,真实的子解析集出现在数学的几个分支,如微分方程和几何。类似的集合类自然出现,例如在数论中,在不同于真实的数的域上,距离的概念具有相当不同的性质。这种域称为非阿基米德域。然而,相应的子解析集与它们的真实的表亲有许多共同的好性质。Lipshitz和罗宾逊将继续他们的调查这些非阿基米德次解析集的性质,使用的方法从数理逻辑,交换代数和代数几何。在非阿基米德的情况下发展了理论的关键要素,他们提出应用他们的想法来扩展这些结果适用的领域。 特别是,他们计划将在非阿基米德环境中发展的思想应用于真实的情况,从而扩大了可以通过这些方法建立良好几何属性的真实的集合的类别。由于用于提取这些集合的几何信息的许多程序在不同领域之间没有变化,他们还计划仔细研究这种一致性的性质。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Leonard Lipshitz其他文献

Leonard Lipshitz的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Leonard Lipshitz', 18)}}的其他基金

Model Theory and Cell Decomposition for Valued Fields with Analytic Structure
具有解析结构的值域的模型理论和元胞分解
  • 批准号:
    0401175
  • 财政年份:
    2004
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant
A Proposal for Vertical Integration of Research and Education in Mathematics and Statistics at Purdue University
普渡大学数学与统计学研究与教育纵向一体化的提案
  • 批准号:
    9983601
  • 财政年份:
    2000
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Model Theory and Rigid Analytic Geometry
数学科学:模型论和刚性解析几何
  • 批准号:
    9704981
  • 财政年份:
    1997
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Rigid Analytic Geometry and Logic
数学科学:刚性解析几何和逻辑
  • 批准号:
    9401451
  • 财政年份:
    1994
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Model Theory, Geometry and Arithmetic
数学科学:模型论、几何与算术
  • 批准号:
    9102858
  • 财政年份:
    1991
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Model Theory and Algebra
数学科学:模型理论和代数
  • 批准号:
    8802410
  • 财政年份:
    1988
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Algebraic Power Series, Differentially Algebraic Power Series and Logic
数学科学:代数幂级数、微分代数幂级数和逻辑
  • 批准号:
    8502780
  • 财政年份:
    1985
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Model Theory of Local Rings; Diophantine Problems For Addition and Divisibility
局环模型理论;
  • 批准号:
    8102689
  • 财政年份:
    1981
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant
Existential Problems For Algebraic Number Rings
代数数环的存在性问题
  • 批准号:
    7606357
  • 财政年份:
    1976
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant

相似国自然基金

Research on Quantum Field Theory without a Lagrangian Description
  • 批准号:
    24ZR1403900
  • 批准年份:
    2024
  • 资助金额:
    0.0 万元
  • 项目类别:
    省市级项目
基于isomorph theory研究尘埃等离子体物理量的微观动力学机制
  • 批准号:
    12247163
  • 批准年份:
    2022
  • 资助金额:
    18.00 万元
  • 项目类别:
    专项项目
Toward a general theory of intermittent aeolian and fluvial nonsuspended sediment transport
  • 批准号:
  • 批准年份:
    2022
  • 资助金额:
    55 万元
  • 项目类别:
英文专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》的翻译
  • 批准号:
    12126512
  • 批准年份:
    2021
  • 资助金额:
    12.0 万元
  • 项目类别:
    数学天元基金项目
基于Restriction-Centered Theory的自然语言模糊语义理论研究及应用
  • 批准号:
    61671064
  • 批准年份:
    2016
  • 资助金额:
    65.0 万元
  • 项目类别:
    面上项目

相似海外基金

Travel: Model Theory of Valued Fields at CIRM
旅行:CIRM 有价值领域的模型理论
  • 批准号:
    2322918
  • 财政年份:
    2023
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant
Model Theory of Valued Differential Fields
值微分场模型论
  • 批准号:
    2154086
  • 财政年份:
    2022
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Continuing Grant
Model theory of expansions of valued fields
有价值领域扩展的模型理论
  • 批准号:
    RGPIN-2016-05431
  • 财政年份:
    2021
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Discovery Grants Program - Individual
Model theory of expansions of valued fields
有价值领域扩展的模型理论
  • 批准号:
    RGPIN-2016-05431
  • 财政年份:
    2020
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Discovery Grants Program - Individual
Model theory of expansions of valued fields
有价值领域扩展的模型理论
  • 批准号:
    RGPIN-2016-05431
  • 财政年份:
    2019
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Discovery Grants Program - Individual
Model Theory of Valued Fields and Applications
有价值领域模型理论及其应用
  • 批准号:
    1922826
  • 财政年份:
    2019
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant
Model theory of expansions of valued fields
有价值领域扩展的模型理论
  • 批准号:
    RGPIN-2016-05431
  • 财政年份:
    2018
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Discovery Grants Program - Individual
Conference/Workshop: Trimester on Model Theory, Combinatorics, and Valued Fields; Spring, 2018; Paris, France
会议/研讨会:模型理论、组合学和值域的三个学期;
  • 批准号:
    1744167
  • 财政年份:
    2017
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Standard Grant
Contributions to the model theory of valued fields
对有价值域模型理论的贡献
  • 批准号:
    1941529
  • 财政年份:
    2017
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Studentship
Model theory of expansions of valued fields
有价值领域扩展的模型理论
  • 批准号:
    RGPIN-2016-05431
  • 财政年份:
    2017
  • 资助金额:
    $ 17.55万
  • 项目类别:
    Discovery Grants Program - Individual
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了