By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

中文翻译：

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拓扑在模型理论中的两种应用

通过使用拟紧凑性的拓扑概念，我们简化和改进了Caicedo，Dueñez和Iovino关于Terence Tao的亚稳性的证明。通过开发将拓扑空间转换为抽象逻辑的机器，我们还查明了遗漏类型定理和Baire类别定理之间的确切关系。