Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Generic sets dependent on Power Set axiom appear mostly in esoteric areas, logic of Set Theory (ST), etc. Recognizing internal to math (formula-specified) and external (based on parameters in those formulas) aspects of sets greatly simplifies the 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. have only finite Kolmogorov Information about them. This allows elimination of all non-integer quantifiers in ST formulas.

翻译：通常的数学集合具有特殊类型：可数集、紧致集、开集、偶尔出现的波莱尔集、罕见的射影集等。依赖于幂集公理的泛型集合主要出现在深奥领域（如集合论逻辑）中。识别集合的内部（公式指定）和外部（基于公式中的参数）方面可极大简化基础理论。我假定外部集合（非内部指定，视为变量域）是遗传可数且独立于公式定义类，即仅包含有限的关于它们的柯尔莫哥洛夫信息。这允许在集合论公式中消除所有非整数量化子。