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FORCING AND THE HALPERN–LÄUCHLI THEOREM
The Journal of Symbolic Logic ( IF 0.6 ) Pub Date : 2019-09-09 , DOI: 10.1017/jsl.2019.59
NATASHA DOBRINEN , DANIEL HATHAWAY

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.

中文翻译:

强迫和 HALPERN-LÄUCHLI 定理

我们研究了各种强迫对几种形式的 Halpern-Läuchli 定理的影响。对于人迹罕至的κ,我们证明它们是由大小小于的强迫保留的κ. 将此与 Zhang 在 [17] 中的工作相结合,得出与有限乘积相关的极化分配关系κ-有理数被所有大小小于的强制保留κ在满足 Halpern–Läuchli 定理的模型上κ. 我们还证明了 Halpern-Läuchli 定理由 <κ-闭合强迫假设κ是可测量的,遵循一些观察到的反射特性。
更新日期:2019-09-09
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