论文标题
在无法访问的红衣主教的产品上近似钻石原理
Approximating diamond principles on products at an inaccessible cardinal
论文作者
论文摘要
我们分离\ emph {近似钻石原理}，这是钻石原理在无法接近的基本主教处的后果。我们使用这些原理来找到否定大型红衣主教钻石原理的新方法。最值得注意的是，我们证明，使用Gitik的重叠扩展器强迫，这是一种新方法，以使钻石原理在大型Cardinal $θ$上的失败而无需更改Cofinalities或将快速俱乐部添加到$θ$。此外，我们表明近似钻石原理必然保持在弱紧凑的红衣主教处。该结果与以下事实相结合：在所有已知模型中，钻石原理失败了近似的钻石原理在不可访问的基本主教处也失败了，它表现出必不可少的组合障碍，使钻石原理在弱紧凑的基本主教处失败。
We isolate \emph{the approximating diamond principles}, which are consequences of the diamond principle at an inaccessible cardinal. We use these principles to find new methods for negating the diamond principle at large cardinals. Most notably, we demonstrate, using Gitik's overlapping extenders forcing, a new method to get the consistency of the failure of the diamond principle at a large cardinal $θ$ without changing cofinalities or adding fast clubs to $θ$. In addition, we show that the approximating diamond principles necessarily hold at a weakly compact cardinal. This result, combined with the fact that in all known models where the diamond principle fails the approximating diamond principles also fail at an inaccessible cardinal, exhibits essential combinatorial obstacles to make the diamond principle fail at a weakly compact cardinal.
