cofinality-$ω$ 可构造模型中测度短序列的模型
Models for short sequences of measures in the cofinality-$ω$ constructible model
AI总结：
研究cofinality-$ω$可构造模型$C^{*}$与测度短序列的关系，证明核心模型包含于$C^{*}$，计算特定模型中的$C^{*}$，并证明内部模型的存在性可传递至$C^{*}$。
摘要：
我们研究 $C^{*}$（使用一阶逻辑扩展以“cofinality-$ω$”量词可构造的集合模型）与测度“短”序列（即阶为 $1$ 且长度小于其最小值的测度序列）之间的关系。我们证明，某些用于测度短序列的核心模型包含在 $C^{*}$ 中；我们在形如 $L\left[\mathcal{U}\right]$ 的模型中计算 $C^{*}$，其中 $\mathcal{U}$ 是测度短序列；并在形如 $L\left[\mathcal{U}\right]\left[G\right]$ 的模型中计算 $C^{*}$，其中 $G$ 是向 $\mathcal{U}$ 的某些可测基数添加 Prikry 序列的泛型；并证明，若存在具有序型 $χ$ 的测度短序列的内部模型，则 $C^{*}$ 中亦存在这样的内部模型。
英文摘要：
We investigate the relation between $C^{*}$, the model of sets constructible using first order logic augmented with the "cofinality-$ω$" quantifier, and "short" sequences of measures - sequences of measures of order $1$, which are shorter than their minimum. We show that certain core models for short sequences of measures are contained in $C^{*}$; we compute $C^{*}$ in a model of the form $L\left[\mathcal{U}\right]$ where $\mathcal{U}$ is a short sequence of measures, and in models of the form $L\left[\mathcal{U}\right]\left[G\right]$ where $G$ is generic for adding Prikry sequences to some of the measurables of $\mathcal{U}$; and prove that if there is an inner model with a short sequence of measures of order type $χ$, then there is such an inner model in $C^{*}$.
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