o-minimal理论中的支配幺半群

亨泽尔赋值域中的支配幺半群

The domination monoid in henselian valued fields

本文研究亨泽尔赋值模型论中各类结构的支配幺半群，在一般设定下建立Ax-Kochen-Ershov型归约，并对具体情形给出完整计算。

稠密交树的弱二元展开

Weakly binary expansions of dense meet-trees

本文通过证明稠密交树理论DMT及其若干二元关系展开的弱二元性，计算并描述了这些理论的支配幺半群，并利用展开关系的支配幺半群给出刻画。

不稳定理论中的随机性和控制

Orthogonality and domination in unstable theories

在本文的第一部分中，我们研究正交性，支配，重量，经常和最小的玫瑰和超玫瑰理论的背景下类型。然后，我们试图为任意相关理论发展类似理论。

Arities and aritizabilities of group, monoid and groupoid theories

We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group $G$ is aritizable if and only if $G$ is finite. It is shown that this criterion does not hold for monoids/groupoids: there is an infinite monoid/groupoid having a binary theory.

Regular S-acts with primitive normal and antiadditive theories

In this work, we investigate the commutative monoids over which the axiomatizable class of regular S-acts is primitive normal and antiadditive. We prove that the primitive normality of an axiomatizable class of regular S-acts over the commutative monoid S is equivalent to the antiadditivity of this class and it is equivalent to the linearity of the order on a semigroup R such that an S-act SR is a maximal (under the inclusion) regular subact of the S-act SS.

Alonzo中的幺半群理论：简单类型理论中的小理论形式化

Monoid Theory in Alonzo: A Little Theories Formalization in Simple Type Theory

本文以幺半群理论为例，展示了如何利用小理论方法在Alonzo逻辑系统中形式化数学知识，采用不完全形式化证明的替代方法以侧重于交流性和可访问性。