We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals satisfying mild set-theoretic hypotheses. This had previously been open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories.

我们使用精确饱和度来研究不稳定理论的复杂性，表明该概念的一个变体称为伪初等类 (PC)-精确饱和度有意义地反映了组合分界线。我们研究 PC 精确饱和度以获得稳定和简单的理论。在其他结果中，我们表明 PC 精确饱和表征了稳定基数的大小至少是可数稳定理论的连续统，此外，简单的不稳定理论在满足温和集合论假设的奇异基数处具有 PC 精确饱和。这以前甚至对于随机图都是开放的。我们根据在可数共尾性的奇异基数处具有 PC 精确饱和来描述可数理论的超简单性。我们还考虑了 PC 精确饱和度的局部模拟，