AI 中文总结
该研究在正则基数κ的后继处，通过Krueger的带模型边条件的力迫迭代技术，力迫使极弱俱乐部猜测与℧原则同时失效，且ω₁处的失效是PFA的已知结果。
AI 中文摘要
从ZFC模型出发，我们对任意正则基数κ，在S_κ^{κ⁺处力迫使极弱俱乐部猜测和℧原则同时失效。该结果采用Krueger提出的、将模型作为边条件的力迫迭代技术得到。在ω₁处，这些原则的失效是PFA的已知结果。
英文摘要
Starting from a model of $\mathrm{ZFC}$, we force the simultaneous failure of the Very Weak Club Guessing and the $\mho$ principles at $S_κ^{κ^+}$, for any regular cardinal $κ$. Our results are obtained by means of a forcing iteration technique, due to Krueger, that incorporates models as side conditions. At $ω_1$, the failure of these principles is a well-known consequence of $\mathrm{PFA}$.
CommentsThe claimed proofs contain an error
