论文标题
接近布里斯托尔模型
Approaching a Bristol model
论文作者
论文摘要
Bristol模型是$ l [C] $的内部模型，其中$ c $是Cohen Real，它不可用一组构造。这个想法是在2011年在布里斯托尔举行的一个研讨会上开发的，但仅由作者在[8]中详细撰写。本文是那些希望对建筑更广泛看法的人的指南。我们尝试提供更多的直觉，该直觉可能是对这种建筑感兴趣的人和$ \ Mathsf {ZF} $的奇数型号的跳跃板。我们还纠正了原始论文中的一些小问题，并证明了新的结果。例如，布里斯托尔模型中的布尔素数理想定理失败，因为某些集合不能线性排序，并且地面模型在其Bristol扩展中始终是可以定义的。除此之外，我们还包括有关Kinna-Wagner原则的讨论，我们认为这可能在理解$ \ Mathsf {ZF} $中的通用多宇宙中起重要作用。
The Bristol model is an inner model of $L[c]$, where $c$ is a Cohen real, which is not constructible from a set. The idea was developed in 2011 in a workshop taking place in Bristol, but was only written in detail by the author in [8]. This paper is a guide for those who want to get a broader view of the construction. We try to provide more intuition that might serve as a jumping board for those interested in this construction and in odd models of $\mathsf{ZF}$. We also correct a few minor issues in the original paper, as well as prove new results. For example, that the Boolean Prime Ideal theorem fails in the Bristol model, as some sets cannot be linearly ordered, and that the ground model is always definable in its Bristol extensions. In addition to this we include a discussion on Kinna--Wagner Principles, which we think may play an important role in understanding the generic multiverse in $\mathsf{ZF}$.
