论文标题
简单和稳定理论的伪元素类中的精确饱和度
Exact saturation in pseudo-elementary classes for simple and stable theories
论文作者
论文摘要
我们研究了稳定和简单理论的PC止饱和度。除其他结果外，我们还表明，PC-液化饱和度表征了至少可计数稳定理论的稳定性红衣主教的稳定性红衣主教，此外，简单的不稳定理论在奇异的红衣主教处具有PC-extact饱和度，满足了温和的固定理论假设，以前对于随机图即可开放。我们表征了可数理论的超图，这是在可数的辅助性的奇异基础上具有PC-抗饱和度。我们还考虑了PC-脱离饱和度的局部类似物，表明局部的PC-效果饱和度的奇异辅助性是SuperShort理论的特征。
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, which 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 analogue of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories.
