论文标题
对象发生器，类别和日常设置理论
Object generators, categories, and everyday set theory
论文作者
论文摘要
在“对象发生器，放松的集合和数学基础”中，我们介绍了``对象生成器''，这是一个比集理论更一般的逻辑环境。在其中，我们发现了集合理论的“轻松”版本。该论文的重点是构建通用的Zermillo-Fraenkel-Choice理论，并且仅凭它与主流数学实践是一致的论点。本文针对潜在用户。 第一个主题是，如果不需要一般上下文，那么对集合理论的描述就会更简单。特别是，这仅使用熟悉的二进制逻辑，并且重新释放几乎与na \“”集理论相同。 第二个主题收集了关于不是集合的最小对象的事实（传统的序数数或``所有集合''）。已知很多，但在很大程度上涉及非二元断言逻辑。例如，该对象的功率集是有界亚对象的不相交联合和Cofinal子对象。但是，{是，否}都没有功能来检测该分解。 第三个主题说明了一般对象生成器上下文如何实现自然和完整精确的工作。
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is focused on construction of the universal Zermillo-Fraenkel-Choice theory, and the argument that it alone is consistent with mainstream mathematical practice. This paper is oriented toward potential users. The first topic is that if the general context is not needed then there is a simpler description of the set theory. In particular this uses only familiar binary logic, and the resut is almost the same as na\"ıve set theory. The second topic collects facts about the smallest object that is not a set (the traditional Ordinal numbers, or ``class of all sets''). Quite a bit is known, but it heavily involves non-binary assertion logic. For instance the powerset of this object is the disjoint union of the bounded subobjects, and the cofinal subobjects. However there is no function to {yes, no} that detects this decomposition. The third topic illustrates how the general object-generator context enables natural and full-precision work with categories.
