正则公理（也叫做基础公理）是 Zermelo-Fraenkel 集合论的公理之一。在一阶逻辑中，这个公理可叙述如下：

翻译为较容易理解的说法就是：

从这个公理可得出两个结果，其一为“不存在以自身为元素的集合”，其二为“没有无限串行 a_n 使得对于所有 i，a_i+1 是 a_i 的元素”。

通过选择公理可以证明后者的逆命题也成立：如果这样的无限串行不存在，则正则公理为真。所以在假定选择公理的情况下，两个陈述是等价的。

正则公理被认为是Zermelo-Fraenkel 集合论中应用最少的公理，因为数学分支中的所有关键性结果都可用集合论中的其他公理证明得到。另外，不包含正则公理的康托的集合论，实际上假定了以自身为一个元素的集合（真类）的存在。

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads:

The axiom implies that no set is an element of itself, and that there is no infinite sequence (a_n) such that a_i+1 is an element of a_i for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true. Hence, the axiom of regularity is equivalent, given the axiom of dependent choice, to the alternative axiom that there are no downward infinite membership chains.