An effectively given initial semigroup (Q1061863)

A domain D (i.e., a conditionally complete and directed-set complete poset with a countable base) together with a continuous, associative binary operation on D is called a semigroup domain. It is effectively given provided that both D is effectively given, and the relation \(e_ i\leq e_ j\circ e_ k\) is recursive (for a base \(\{e_ 0,e_ 1,e_ 2,...\})\). The paper presents a deep proof that the free semigroup domains on finitely many generators are effectively given.