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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
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
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