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arXiv math/0605448math.LO
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K(R)的尺度和精细结构。部分II:弱真小鼠和天平

Scales and the fine structure of K(R). Part II: Weak real mice and scales

D. W. Cunningham

摘要:

定义了弱实小鼠$\mathcal{M}$,证明了当$m$是最小整数$m>0$使得$\boldsymbolΣ_m(\mathcal{M})$包含一个不在$\mathcal{M}$中的实数集时,黑体点类$\boldsymbolΣ_m(\mathcal{M})$具有仅假设$\mathcal{M}$中实数集的确定性的标度性质.我们将在第三部分中使用这种发展来获得$K(\mathbb{R})$中复杂性最小的规模。

英文摘要:

We define weak real mice $\mathcal{M}$ and prove that the boldface pointclass $\boldsymbolΣ_m(\mathcal{M})$ has the scale property assuming only the determinacy of sets of reals in $\mathcal{M}$ when $m$ is the smallest integer $m>0$ such that $\boldsymbolΣ_m(\mathcal{M})$ contains a set of reals not in $\mathcal{M}$. We shall use this development in Part III to obtain scales of minimal complexity in $K(\mathbb{R})$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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