Forcing and the Halpern-Lauchli Theorem
Forcing and the Halpern-Lauchli Theorem
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强迫和 Halpern-Lauchli 定理
DOI：
10.1017/jsl.2019.59
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Hathaway, Daniel
中科院分区：
文献类型：
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作者：
Dobrinen, Natasha;Hathaway, Daniel
我们研究了各种强迫对几种形式的Halpern-Läuchli定理的影响。对于不可达的κ，我们证明了它们被大小小于κ的力所保持。将此结果与Zhang在[17]中的工作相结合，得出与κ-有理数的有限乘积相关的极化配分关系被在κ处满足Halpern-Läuchli定理的模型上的所有小于κ的力所保持。我们还证明了Halpern-Läuchli定理是由<κ-闭强迫假设κ是可测的，下面一些观察到的反射性质。
We investigate the effects of various forcings on several forms of the Halpern– Läuchli theorem. For inaccessible κ, we show they are preserved by forcings of size less than κ. Combining this with work of Zhang in [17] yields that the polarized partition relations associated with finite products of the κ-rationals are preserved by all forcings of size less than κ over models satisfying the Halpern– Läuchli theorem at κ. We also show that the Halpern–Läuchli theorem is preserved by <κ-closed forcings assuming κ is measurable, following some observed reflection properties.