Serialisation Sequence

A serialisation sequence is a sequence $(S_1, \ldots, S_n)$ such that $S_1$ is an initial set of $F$ and each $S_i$ with $2 \le i \le n$ is an initial set of the reduct $F^{S_1 \cup \ldots \cup S_{i-1}}$.

Remarks

A non-empty set is admissible iff it is the union $S_1 \cup \ldots \cup S_n$ of some serialisation sequence (Thimm, 2022).