论文标题
无选的大型红衣主教和固定理论的潜在主义
Choiceless large cardinals and set-theoretic potentialism
论文作者
论文摘要
我们定义了ZF结构的潜在主义系统，即通过二进制可访问性关系连接的ZF语言的可能世界的集合，实现了整个背景设置理论宇宙$ V $的潜在主义帐户。该定义涉及伯克利枢机主教，这是最强的已知大型基本公理，与选择的公理不一致。实际上，作为背景理论，我们只是假设ZF。事实证明，在我们系统的每个世界上都是有效的命题模态主张，正是模态理论中的命题断言。此外，我们表征了满足潜在主义最大程度原则的世界，因此是模态理论S5，均以ZF语言的主张以及在全部潜在主义语言中的主张。
We define a potentialist system of ZF-structures, that is, a collection of possible worlds in the language of ZF connected by a binary accessibility relation, achieving a potentialist account of the full background set-theoretic universe $V$. The definition involves Berkeley cardinals, the strongest known large cardinal axioms, inconsistent with the Axiom of Choice. In fact, as background theory we assume just ZF. It turns out that the propositional modal assertions which are valid at every world of our system are exactly those in the modal theory S4.2. Moreover, we characterize the worlds satisfying the potentialist maximality principle, and thus the modal theory S5, both for assertions in the language of ZF and for assertions in the full potentialist language.
