Completion

A completion of an iAF $I = (A, A^?, R, R^?)$ is an AF $F^* = (A^*, R^*)$ with $A \subseteq A^* \subseteq A \cup A^?$ and $R|_{A^*} \subseteq R^* \subseteq (R \cup R^?)|_{A^*}$, where $X|_{A^*} = X \cap (A^* \times A^*)$.