 Addison observed (1958, 1959) that these classical definitions can be effectivized by restricting to computable unions in the definition of the \(\mathbf{\Sigma^0_n}\) sets. This leads to the so-called lightface version of the Borel hierarchy—customarily denoted using the same notations \(\Sigma^0_n\) and \(\Pi^0_n\) used for the levels of arithmetical hierarchy—and corresponding definitions of \(\Sigma^1_1\) (i.e., lightface analytic), \(\Pi^1_1\) (i.e., lightface co-analytic), and \(\Delta^1_1\) sets. In particular, this sequence of definitions suggests an analogy between  Theorem 3.15  and the following classical result of Suslin: