强相依理论的秩

强极小理论的无穷大强迫与二元半孤立公式的分布代数

Forcing of infinity and algebras of distributions of binary semi-isolating formulas for strongly minimal theories

我们应用的一般方法分布的二元隔离和半隔离公式的类强极小理论。

NSOP$_1$理论中的传递性、低度性与秩

Transitivity, lowness, and ranks in NSOP$_1$ theories

本文在满足存在性公理的NSOP$_1$理论中研究Kim-独立性，证明其传递性及$\ind^{K}$-Morley序列见证Kim-分叉，并推出低度理论中Shelah与Lascar强类型重合，同时提出新的秩概念。

Distality Rank

Building on Pierre Simon's notion of distality, we introduce distality rank as a property of first-order theories and give examples for each rank $m$ such that $1\leq m \leq ω$. For NIP theories, we show that distality rank is invariant under base change. We also define a generalization of type orthogonality called $m$-determinacy and show that theories of distality rank $m$ require certain products to be $m$-determined. Furthermore, for NIP theories, this behavior characterizes $m$-distality. If we narrow the scope to stable theories, we observe that $m$-distality can be characterized by the …

非超稳定理论强等价非同构模型的构造。B部分

Constructing strongly equivalent nonisomorphic models for unsuperstable theories. Part B

我们研究如何等价的非同构模型的非超稳定理论可以。我们衡量的等价性Eschericht-Fraisse游戏。本文继续[HySh：474]。

On rank not only in NSOP1 theories

We introduce a family of local ranks DQ depending on a finite set Q of pairs of the form (φ(x,y),q(y)) where φ(x,y) is a formula and q(y) is a global type. We prove that in any NSOP1 theory these ranks satisfy some desirable properties; in particular, DQ(x=x)<ωfor any finite variable x and any Q, if q\supseteq p is a Kim-forking extension of types, then DQ(q)<DQ(p) for some Q, and if q\supseteq p is a Kim-non-forking extension, then DQ(q)=DQ(p) for every Q that involves only invariant types whose Morley powers are \ind^K-stationary. We give natural examples of families of invariant types satis…

一些简单秩一理论中的剪切

Shearing in some simple rank one theories

本文刻画了随机图的剪切性质，并利用剪切区分随机图与高阶无三角形随机图理论 $T_{n,k}$，证明剪切在简单不稳定秩一理论中不同于划分且具有分类意义。

非超稳定理论的强等价非同构模型的构造，A部分

Constructing strongly equivalent nonisomorphic models for unsuperstable theories, Part A

我们研究如何等价的非同构模型的非超稳定理论可以有。我们衡量的等价性Eschericht-Fraisse游戏。

非超稳定理论的强等价非同构模型的构造，C部分

Constructing strongly equivalent nonisomorphic models for unsuperstable theories, Part C

本文证明了具有dop的稳定理论T的kappa（T）-饱和模型的一个强非结构定理。

简单理论中分叉的几何学

Geometry of forking in simple theories

研究了超单w-范畴理论中U-秩2元分叉的几何性质，证明了这类元的稳定分叉和一些结构性质。我们将这种分析扩展到U秩3元素的情况。

强相依理论

Strongly dependent theories

我们进一步研究了强相依（一阶完全）理论T的模型类，继续数学。LO/0406440。如果|A| + |T| <= μ，I子集C，|I| >= beth_{|T|^+}（μ），则基数μ ^+的某个J子集I是A上的不可分辨序列。

Recursive spectra of flat strongly minimal theories

We show that for a model complete strongly minimal theory whose pregeometry is flat, the recursive spectrum (SRM($T$)) is either of the form $[0,α)$ for $α\in ω+2$ or $[0,n]\cup\{ω\}$ for $n\in ω$, or $\{ω\}$, or contained in $\{0,1,2\}$. Combined with previous results, this leaves precisely 4 sets for which it is not yet determined whether each is the spectrum of a model complete strongly minimal theory with a flat pregeometry.

满足Zilber剖分的强极小理论的递归谱

Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy

我们猜想，对于满足Zilber三分性的有限签名中的强极小理论T，T的递归谱只有三种可能：T的所有可数模型都是递归可表示的;它们都不是递归可表示的;或者只有T的零维模型是递归可表示的.我们证明了这一猜想分解（以前，平凡）的理论和模群。该猜想也通过已知的领域的结果。该猜想仍然开放的有限覆盖的群体和领域。

Strongly Minimal Sets and Categoricity in Continuous Logic

The classical Baldwin-Lachlan characterization of uncountably categorical theories is known to fail in continuous logic in that not every inseparably categorical theory has a strongly minimal set. Here we investigate these issues by developing the theory of strongly minimal sets in continuous logic and by examining inseparably categorical expansions of Banach space. To this end we introduce and characterize 'dictionaric theories,' theories in which definable sets are prevalent enough that many constructions familiar in discrete logic can be carried out. We also introduce, in the context of Ban…

至多具有可数个非同构生成模型的理论的生成模型

On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models

我们研究可数理论的非同构生成模型，最多有可数个非同构的非同构生成模型。引入了非同构生成模型的秩的概念，证明了当T至多有可数个非同构的非同构生成模型时，每个非同构生成模型都有序秩.利用这一秩给出了类似于群的Hopf性质的群生成模型的一个性质，并给出了群生成模型是其完备理论的素的一个充要条件.研究了方程诺特群的极限群的秩的一些性质。

具有强嵌入子群的有限Morley秩的极小连通单群

Minimal connected simple groups of finite Morley rank with strongly embedded subgroups

证明了有限Morley秩的极小非代数单群的Prufer秩至多为2，从而消除了Cherlin和Jaligot关于极小单群的工作中的驯服性.这里给出的论证是从Borovik、Burdges和Nesin的强嵌入极小简单构形开始的。Burdges论文中的0-uniform机器被用来分析涉及博雷尔子群的非交换交集的构形。Cherlin和Jaligot的数论妙语已经被一个新的泛型参数所取代。

奇型群的强嵌入子群

Strongly Embedded Subgroups of Groups of Odd Type

本文证明了有限Morley秩奇型K ~*-群G的任何不解释坏域的强嵌入子群是可解的，如果它的Pruefer 2-秩至少为2。如果G的正规2-秩至少为3，这有两个重要的结果：如果G包含一个对合的不可解中心化子，则G不包含任何真2-生成核，且对合的中心化子有平凡核。

独角兽的不存在性与多类 Löwenheim-Skolem 定理

The nonexistence of unicorns and many-sorted Löwenheim-Skolem theorems

本文证明了可满足性模理论中“独角兽理论”不存在，即稳定无穷且强有限可见证的理论必是强礼貌的，并证明了多类逻辑的 Löwenheim-Skolem 定理与 Łoś-Vaught 测试版本。

dp秩的可加性

Additivity of the dp-rank

本文的主要结果是dp-秩的次可加性。证明了有限dp-秩理论的研究不能归结为对它的dp-极小型的研究，并讨论了dp-秩与VC-密度之间的可能关系。