论文标题
Zermelo-Fraenkel Axioms，内部类，外部集合
Zermelo-Fraenkel Axioms, Internal Classes, External Sets
论文作者
论文摘要
通常的数学集具有特殊类型：可计数，紧凑，开放，偶尔是骨，很少投影等。它们是由单个集合理论公式描述的，该公式与其他公式无关的参数。涉及与无限复杂性或与Powerset公理公式相关的集合的外来表达式出现在深奥或基础研究中。 识别数学内部（公式指定）和外部（基于这些公式中的参数）数学对象方面极大地简化了基础。我假定外部集合（未内部指定，被视为变量的域）是遗传性可计数的，并且独立于公式定义的类，即使用有限的kolmogorov信息。这允许在集合理论语句中消除所有非量化量子量子。
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. They are described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving sets related to formulas of unlimited complexity or to Powerset axiom appear mostly in esoteric or foundational studies. Recognizing internal to math (formula-specified) and external (based on parameters in those formulas) aspects of math objects greatly simplifies foundations. I postulate external sets (not internally specified, treated as the domain of variables) to be hereditarily countable and independent of formula-defined classes, i.e. with finite Kolmogorov Information about them. This allows elimination of all non-integer quantifiers in Set Theory statements.
