结构的内聚幂

ω在Δ₂凝聚集及无Δ₂凝聚子集的无限Π₁集上的有效幂

Effective powers of $ω$ over $Δ_2$ cohesive sets and infinite $Π_1$ sets without $Δ_2$ cohesive subsets

该研究证明存在ω的可计算副本，其在所有Δ₂凝聚集上的凝聚幂具有序型ω+η，还构造了无Δ₂ p-凝聚子集的无限Π₁集，改进了相关早期结果。

On cohesive powers of linear orders

Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let $ω$, $ζ$, and $η$ denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of $ω$. If $\mathcal{L}$ is a computable copy of $ω$ that is computably isomorphic to the usual presentation of $ω$, then every cohesive power of $\mathcal{L}$ has order-type $ω+ ζη$. However, there are computable cop…

凝聚幂的坦南鲍姆型定理

Tennenbaum-like theorems for cohesive powers

该研究针对凝聚幂构造，构造了特定图与线性序，分别得到凝聚幂具有度0''、无计算表示的结果，为凝聚幂的编码能力提供了坦南鲍姆型定理相关结论。

Cohesive Powers of Linear Orders

Cohesive powers of computable structures can be viewed as effective ultraproducts over effectively indecomposable sets called cohesive sets. We investigate the isomorphism types of cohesive powers $Π_{C}% \mathcal{L}$ for familiar computable linear orders $\mathcal{L}$. If $% \mathcal{L}$ is isomorphic to the ordered set of natural numbers $\mathbb{N}$ and has a computable successor function, then $Π_{C}\mathcal{L}$ is isomorphic to $\mathbb{N}+\mathbb{Q}\times \mathbb{Z}.$ Here, $+$ stands for the sum and $\times $ for the lexicographical product of two orders. We construct computable linear …

关于字段的积

On Cohesive Products of Fields

本文研究了有效超积的理论及其伽罗华群，探讨了有限和无限伽罗华扩张中 cohesive 产品与伽罗华群的相互作用，并介绍了超自同构群。

可定义群的正交分解

Orthogonal decomposition of definable groups

本文在模型论中引入内聚性概念以刻画可定义集内部交互，并证明 o-minimal 结构中的可定义群可分解为内聚正交子集的乘积，同时探讨了特定条件下的内聚性及阿贝尔群的结构。