递归可枚举集合（英语：Recursively enumerable set）是可计算性理论或更狭义的递归论中的一个概念。可数集合S被称为是递归可枚举、计算可枚举的、半可判定的或可证明的，如果

或者等价的说，

包含所有可递归枚举集合的复杂性类是 RE。

共同的编程意义会暗示出如何转换一种算法到等价的另一种算法。第一种情况说明了为什幺有时说半可判定的，而第二种情况说明了为什幺叫计算可枚举的。

In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if:

Or, equivalently,

The first condition suggests why the term semidecidable is sometimes used; the second suggests why computably enumerable is used. The abbreviations r.e. and c.e. are often used, even in print, instead of the full phrase.