 This definition extends the definition of a primitive recursive relation given in  Section 2.1—e.g.,  since sets like PRIMES and DIV are primitive recursive they are ipso facto computable. Via Church’s Thesis, the notion of a computable set thus also generalizes the accompanying heuristic about effective decidability—i.e., \(R\) is computable just in case there is an algorithm for deciding if \(R(\vec{n})\) holds which always returns an answer after a finite (although potentially unbounded) number of steps. On the other hand, it follows from the observations recorded in  Section 3.2  that none of HP, K, Z, TOT, or FIN are computable sets.