论文标题
恒星，LELEK粉丝和连续逻辑中非$ \ aleph \ _0 $ - 分类理论的重建
Star sorts, Lelek fans, and the reconstruction of non-$\aleph\_0$-categorical theories in continuous logic
论文作者
论文摘要
我们证明了一种以可数语言的连续（或经典）逻辑中任意理论有效的重建定理，也就是说，我们以开放的波兰拓扑类型的形式为这些理论提供了完整的双重介绍不变。 更明确的是，对于每个这样的理论$ t $，我们构建了一个仅取决于$ t $的双交易类别的groupoid $ \ mathbf {g}^*（t）$，相反，我们从$ \ mathbf {g}^*（t）理论中重建了与$ t $相比的理论。 $ \ Mathbf {g}^*（t）$的基础（即，当被视为类别时的对象集）始终是LELEK FAN的同型。 我们将不变的构造分为两个步骤。 在第二步中，我们从任何\ emph {重建排序}中构造了一个群体，而在第一步中，构建了这种类型。 这使我们能够将结果置于一个以前建立的框架的共同框架中，这只会因其不同选择重建排序而有所不同。
We prove a reconstruction theorem valid for arbitrary theories in continuous (or classical) logic in a countable language, that is to say that we provide a complete bi-interpretation invariant for such theories, taking the form of an open Polish topological groupoid. More explicitly, for every such theory $T$ we construct a groupoid $\mathbf{G}^*(T)$ that only depends on the bi-interpretation class of $T$, and conversely, we reconstruct from $\mathbf{G}^*(T)$ a theory that is bi-interpretable with $T$. The basis of $\mathbf{G}^*(T)$ (namely, the set of objects, when viewed as a category) is always homeomorphic to the Lelek fan. We break the construction of the invariant into two steps. In the second step we construct a groupoid from any \emph{reconstruction sort}, while in the first step such a sort is constructed. This allows us to place our result in a common framework with previously established ones, which only differ by their different choice of a reconstruction sort.
