Lovely pairs of models: the non first order case

Lovely pairs for independence relations

In the literature there are two different notions of lovely pairs of a theory T, according to whether T is simple or geometric. We introduce a notion of lovely pairs for an independence relation, which generalizes both the simple and the geometric case, and show how the main theorems for those two cases extend to our general notion.

On supersimplicity and lovely pairs of cats

We prove that the definition of supersimplicity in metric structures from \cite{pezz:Morley} is equivalent to an \textit{a priori} stronger variant. This stronger variant is then used to prove that if $T$ is a supersimple Hausdorff cat then so is its theory of lovely pairs.

可消除的可爱对强几何域

Quantifier elimination for lovely pairs of strongly geometric fields

本文研究了强几何域的可爱对理论，证明其在定义扩展下具有可消除性，并作为特殊情况获得了实闭域和p-进闭域理论的可消除性。

简单理论中广义拼接的转移

Transfer of generalized amalgamation in simple theories

本文提出一个抽象框架，将简单理论中的广义拼接性质转移到其他理论中，并应用于有界PAC结构、带有运算的字段和可爱对理论。主要贡献是证明有界伪代数闭字段无论其不完美程度如何都具有广义拼接性质。

关于第一类树性质缺失理论的一个保持定理

A preservation theorem for theories without the tree property of the first kind

本文证明了几何理论的NTP$_1$性质在可爱对和$H$-结构中保持，并给出非简单几何NTP$_1$理论的例子。

On the forking topology of a reduct of a simple theory

Let $T$ be simple and $T^-$ a reduct of $T$. For variables $x$, we call an $\emptyset$-invariant set $Γ(x)$ of ${\cal C}$ with the property that for every formula $ϕ^-(x,y)\in L^-$: for every $a$, $ϕ^-(x,a)$ $L^-$-forks over $\emptyset$ iff $Γ(x)\wedge ϕ^-(x,a)$ $L$-forks over $\emptyset$, a \em universal transducer\em. We show that there is a greatest universal transducer $\tildeΓ_x$ (for any $x$) and it is type-definable. In particular, the forking topology on $S_y(T)$ refines the forking topology on $S_y(T^-)$. Moreover, we describe the set of universal transducers in terms of certain topol…