会议时间 Date：2025年9月5日至7日 September 5-7, 2025
会议地点 Location：内蒙古大学桃李湖宾馆 Taolihu Hotel, Inner Mongolia University
主办单位 Host：内蒙古大学数学科学学院 School of Mathematical Sciences, Inner Mongolia University
第24届德尔塔逻辑研讨会旨在促进逻辑学科间交流与合作。诚邀相关领域专家学者参会。The Delta 24 Logic Workshops aim to bring logicians from Mathematics, Philosophy, and Computer Science together.
- 杨文涛 Wentao Yang：ndwyang@imu.edu.cn
| 2025年9月5日（周五）下午 September 5, 2025 Afternoon | |
|---|---|
| 15:30-18:00 | 会议报到：内蒙古大学桃李湖宾馆 Registration at Taolihu Hotel |
| 2025年9月6日（周六）上午 September 6, 2025 Morning 宾馆中书省会议室（四楼） Meeting Room of the Hotel (4th floor) |
|
| 9:30-9:35 | 开场致辞 Opening 嘉宾：张瑞岗 Ruigang Zhang |
| 9:35-10:15 | Forcing construction related to club principle 报告人 Speaker：吴刘臻 Liuzhen Wu |
| Club principle is a weak form of diamond principle. Shelah first introduced a forcing poset separating club and diamond principle. Several similar forcing posets were also studied later. In an ongoing project, we introduce another forcing poset separating club and diamond and discuss its new features and some possible application. | |
| 10:15-10:45 | 合影、茶歇 Group Photo and Tea Break |
| 10:45-11:25 | A Variant of Chaitin's Omega Function
报告人 Speaker：李宇轩 Yuxuan Li |
| This is a joint work with Shuheng Zhang, Xiaoyan Zhang and Xuanheng Zhao. We investigate the continuous function \(f\) defined by \[x\mapsto \sum_{\sigma\le_L x }2^{-K(\sigma)}\] as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we obtain that: (i) \(f\) is differentiable precisely at density random points; (ii) \(f(x)\) is \(x\)-random if and only if \(x\) is weakly low for \(K\) (low for \(\Omega\)); (iii) the range of \(f\) is a null, nowhere dense, perfect \(\Pi^0_1(\emptyset')\) class with Hausdorff dimension \(1\); (iv) \(f(x)\oplus x\ge_T\emptyset'\) for all \(x\); (v) there are \(2^{\aleph_0}\) many \(x\) such that \(f(x)\) is not 1-random; (vi) \(f\) is not Turing invariant but is Turing invariant on the ideal of \(K\)-trivial reals. We also discuss the connection between \(f\) and other variants of Omega. | |
| 11:25-12:05 | 一个与组合数学命题等价的可计算性理论问题
报告人 Speaker：刘路 Lu Liu |
| 我们证明，Miller和Solomon的问题------是否每个有穷长字符序列上的染色c都存在c-可计算的variable word infinite解， 等价于一个组合数学问题。该组合数学问题为是否存在一个无穷长整数序列使得其每个初段都满足一个Ramsey类型的性质。该组合数学问题的 否定，是Hales-Jewett定理的自然推广。 | |
| 12:05-13:30 | Lunch Break |
| 2025年9月6日（周六）下午 September 6, 2025 Afternoon 宾馆中书省会议室（四楼） Meeting Room of the Hotel (4th floor) | |
| 13:30-14:10 | Upside down and backwards
报告人 Speaker: Kyle Gannon |
| We investigate the semigroup of invariant types through the lens of Ellis theory; primarily focusing on definably amenable NIP groups. In the definably amenable NIP context, we observe that the collection of right strong \(f\)-generic types forms the unique minimal left ideal and thus, the Ellis subgroups are isomorphic to the \(G/G^{00}\) via the canonical quotient map. As consequence of the Newelski-Pillay conjecture, the Ellis subgroups of the semigroup of invariant types are abstractly isomorphic to the Ellis subgroups of the semigroup of finitely satisfiable types in the definable amenable NIP setting. We are interested in the existence of \emph{natural isomorphisms} from invariant Ellis subgroups to finitely satisfiable Ellis subgroups and we determine when these isomorphisms can be witnessed by (variants of) Simon's retraction map. We then provide several limiting examples. Outside of the NIP context, we provide an (dfg) abelian group in which the invariant Ellis subgroups and finitely satisfiable Ellis subgroups not isomorphic. This is joint work with Tomasz Rzepecki. | |
| 14:10-14:40 | 茶歇 Tea Break |
| 14:40-15:20 | Revisiting Zilber’s Trichotomy
报告人 Speaker：叶谨赫 Jinhe "Vincent" Ye |
| Zilber's Trichotomy Conjecture remains a central theme in model theory, offering a powerful lens through which to understand the geometry of definable sets in well-behaved contexts. Although numerous counterexamples exist, the conjecture continues to inspire fruitful investigation. In this talk, I will introduce a new axiomatic framework — Hausdorff Geometric Structures — that captures a broad range of contexts where the Trichotomy holds. This framework provides a unified approach to studying the trichotomy in such structures. Using this, we fully resolve the restricted trichotomy conjecture in the theory of algebraically closed fields. The talk is based on joint work with Ben Castle and Assaf Hasson. | |
| 15:20-16:00 | From Plato's Diairesis to Shelah's Dividing Line----The long journey of exploring objective concepts 报告人 Speaker： 郝兆宽 Zhaokuan Hao |
| We are focusing on Plato's method of diairesis. This is a method for discovering definitions of concepts that he developed in a series of dialogues, including Phaedrus, Sophist, Statesman, and Philebus. Interestingly, Gregory Cherlin points out that Saharon Shelah's strategy for dividing lines in contemporary model theory is a mathematical version of Plato's "cutting through the middle." John T. Baldwin puts this more specifically: a dividing line is a property that must be both a "virtuous property" and its negation. In this talk, we will focus on more fundamental philosophical questions: Why do dividing lines exist? How can a philosopher or mathematician be sure that a dividing line has been discovered? The requirements for candidate dividing lines proposed by Shelah and the strategy of using the "test problem" parallel various actual methods of dividing in Plato's dialogues. In essence, these requirements and strategies are actually intended to ensure that Plato's requirement in the Sophist is to divide according to Form, that is, objective concepts as we understand them. | |
| 18:30- | Dinner |
| 2025年9月7日（周日）上午 September 7, 2025 |
|
| 9:00-12:00 | 自由讨论 |