接近布里斯托尔模型
Approaching a Bristol model
AI总结：
本文介绍了布里斯托尔模型的构造，指出其中布尔素理想定理失效，并探讨了金纳-瓦格纳原理在$\mathsf{ZF}$中的潜在作用。
摘要：
布里斯托尔模型是$ L[c] $的一个内模型，其中$c$是一个科恩实数，它不能由一个集合构造出来。该想法是在2011年于布里斯托尔举行的工作坊中提出的，但直到[8]中才被作者详细写出。本文为那些希望获得该构造更全面视图的人提供指南。我们试图提供更多的直觉，这可能成为对这一构造以及奇数$\mathsf{ZF}$模型感兴趣的人的跳板。我们还修正了原始论文中的几个小问题，并证明了新的结果。例如，在布里斯托尔模型中，布尔素理想定理失效，因为某些集合无法线性排序，且地面模型始终可以在其布里斯托尔扩展中被定义。此外，我们还讨论了金纳-瓦格纳原理，我们认为这些原理可能在理解$\mathsf{ZF}$中的通用多元宇宙中发挥重要作用。
英文摘要：
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 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 $\mathsf{ZF}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
