The non‐forking‐instances topology (NFI topology) is a topology on the Stone space of a theory T that depends on a reduct $T^{-}$ of T. This topology has been used in [6] to describe the set of universal transducers for $(T,T^{-})$ (invariants sets that translate forking‐open sets in $T^{-}$ to forking‐open sets in T). In this paper we show that in contrast to the stable case, the NFI topology need not be invariant over parameters in $T^{-}$ but a weak version of this holds for any simple T. We also note that for the lovely pair expansions, of theories with the weak non‐finite cover property (wnfcp), the topology is invariant over $⌀$ in $T^{-}$.

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关于非分叉实例拓扑的说明

的非分叉-实例拓扑（NFI拓扑）是在理论的石空间的拓扑Ť取决于一个简${Ť}^{-}$的牛逼。在[6]中已经使用该拓扑来描述用于$（Ť，{Ť}^{-}）$ （用于翻译分叉开放集的不变量集 ${Ť}^{-}$到T中的分叉开放集。在本文中，我们表明，与稳定情况相比，NFI拓扑不必随参数的变化而不变${Ť}^{-}$但是对于任何简单的T，它的弱版本都适用。我们还注意到，对于具有弱非有限覆盖属性（wnfcp）的理论的可爱对展开，拓扑在$⌀$ 在 ${Ť}^{-}$。