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:2018
- 资助国家:加拿大
- 起止时间:2018-01-01 至 2019-12-31
- 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.
我们建议继续发展不可分数学结构的集合论粗分类理论的项目,并着眼于在周围数学领域的具体应用。这一次我们也想检查它在集合论本身的应用,特别是在连续统问题上的应用。这个层次上的许多粗糙分类问题都涉及到可在可数序数集合上存在的结构,这一集合在连续统问题的任何公式中都起着至关重要的作用,所以这里应该存在一些联系并不奇怪。事实证明,迄今为止发展起来的任何集合论粗结构理论都与最初的康托尔连续统假设背道而驰。事实上,这些理论倾向于对连续统的基数和连续统的其他基数不变量给出相当具体的值,因此我们想从一般的角度来考察这种现象。我们提出的一些具体的粗分类问题是紧Hausdorff空间的基问题和一般Banach空间的可分商问题。特别是,我们想要找到存在于任何足够长的弱零序列中的确切条件结构。结果表明,粗糙集合论分类理论可以很好地与这类经典方法相结合,例如,拉姆齐分类理论和图基分类理论。所以我们项目的一部分也将致力于研究这些联系。事实上,我们最近发现在自然数集上超滤的Tukey分类理论与可数结构的Ramsey理论之间有相当密切的关系。这给我们带来了拉姆齐理论的新问题,这些问题具有独立的利益,并可能有进一步的应用。所以,我们在这个项目中的一部分努力也将致力于发展这种拉姆齐理论。这将是我们发展拉姆齐理论的自然延续,这不仅适用于集合理论,也适用于其他数学领域,例如,超齐次结构自同构群的拓扑动力学。
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
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
Basis Problems in Set Theory
集合论的基础问题
- 批准号:
RGPIN-2014-04184 - 财政年份:2017
- 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: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
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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:
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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:2017
- 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
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RGPIN-2014-04184 - 财政年份:2014
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$ 3.64万 - 项目类别:
Discovery Grants Program - Individual
Basis problems in set theory
集合论的基本问题
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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
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122013-2009 - 财政年份:2012
- 资助金额:
$ 3.64万 - 项目类别:
Discovery Grants Program - Individual