Basis Problems in Set Theory
集合论的基础问题
基本信息
- 批准号:RGPIN-2014-04184
- 负责人:
- 金额:$ 3.64万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2017
- 资助国家:加拿大
- 起止时间:2017-01-01 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
We propose to continue the project of developing a set-theoretic coarse classification theory for non-separable mathematical structures with an eye towards specific applications to surrounding areas of mathematics. This time we would like also to examine its application to set theory itself and in particular to the continuum problem. Many coarse classification problems at this level concern structures that can be put to live on the set of countable ordinals, a set that plays the crucial role in any formulation of the continuum problem so it is not surprising that there should be some connection here at all. As it turns out, any set-theoretic coarse structure theory developed so far goes in the opposite to the original Cantor's Continuum Hypothesis. In fact, these theories tend to give quite specific values to the cardinality of the continuum and other cardinal invariants of the continuum, and so we would like to examinee this phenomena from a general perspective. Some specific coarse classification problems that we propose to work on is the basis problem for compact Hausdorff spaces and the separable quotient problem for general Banach spaces. In particular, we would like to find the exact conditional structure that is present in any sufficiently long weakly null sequence. It turns out that the coarse set-theoretic classification theory goes well with the classical approaches of this kind such as, for example, the Ramsey classification theory and the Tukey classification theory. So part of our project will be devoted towards examining these connections as well. In fact, we have recently discovered that there is a quite close relationship between Tukey classification theory of ultrafilters on the set of natural numbers and the Ramsey theory of countable structures. This is leading us to new problems of Ramsey theory that are of independent interests and are likely to have further applications. So, a part of our efforts during the project will be devoted towards developing this kind of Ramsey theory as well. This will be a natural continuation of our already old project towards developing Ramsey theory this is applicable not only to set theory but also to other surrounding areas of mathematics such as, for example, the topological dynamics of groups of automorphisms of ultrahomogeneous structures.
我们建议继续开发一个集理论的粗分类理论的非可分离的数学结构的项目,着眼于具体应用到周围的数学领域。这一次,我们也想考察它在集合论本身,特别是在连续统问题上的应用。这个层次上的许多粗分类问题都涉及到可以放在可数序数集合上的结构,可数序数集合在连续统问题的任何表述中都起着至关重要的作用,所以这里应该有某种联系也就不足为奇了。事实证明,迄今为止发展的任何集合论粗结构理论都与最初的康托连续统假设相反。事实上,这些理论倾向于给连续统的基数和连续统的其他基数不变量赋予相当具体的值,所以我们想从一般的角度来审视这种现象。一些具体的粗分类问题,我们建议工作的基础问题,紧Hausdorff空间和一般Banach空间的可分商问题。特别是,我们希望找到存在于任何足够长的弱空序列中的精确条件结构。事实证明,粗集理论分类理论与这类经典方法,例如Ramsey分类理论和Tukey分类理论很好。因此,我们项目的一部分也将致力于研究这些联系。事实上,我们最近发现自然数集上的超滤子的Tukey分类理论与Ramsey可数结构理论之间有着相当密切的关系。这就把我们引向了拉姆齐理论的新问题,这些新问题具有独立的意义,而且很可能有进一步的应用。因此,我们在项目期间的一部分工作也将致力于发展这种拉姆齐理论。这将是一个自然的延续,我们已经老项目对发展拉姆齐理论这不仅适用于集理论,但也适用于其他周边地区的数学,如,例如,拓扑动力学群的自同构的超齐次结构。
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)
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Todorcevic, Stevo其他文献
Todorcevic, Stevo的其他文献
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{{ truncateString('Todorcevic, Stevo', 18)}}的其他基金
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2022
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2021
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2020
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2019
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2018
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Canada Research Chair in Mathematics
加拿大数学研究主席
- 批准号:
1000218829-2009 - 财政年份:2017
- 资助金额:
$ 3.64万 - 项目类别:
Canada Research Chairs
Canada Research Chair in Mathematics
加拿大数学研究主席
- 批准号:
1000218829-2009 - 财政年份:2016
- 资助金额:
$ 3.64万 - 项目类别:
Canada Research Chairs
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2016
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2015
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Canada Research Chair in Mathematics
加拿大数学研究主席
- 批准号:
1218829-2009 - 财政年份:2015
- 资助金额:
$ 3.64万 - 项目类别:
Canada Research Chairs
相似海外基金
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2022
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2021
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2020
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2019-04311 - 财政年份:2019
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2018
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2016
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2015
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2014
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis problems in set theory
集合论的基本问题
- 批准号:
122013-2009 - 财政年份:2013
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis problems in set theory
集合论的基本问题
- 批准号:
122013-2009 - 财政年份:2012
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual