Definition 6

— Let $L$ be an extension of a field $K$ and $(E_i)_{i \in I}$ a family of subextensions of $L$. The family $(E_i)_{i \in I}$ is said to be algebraically free if the following condition is satisfied:

(AF) For each $i \in I$ let $A_i$ be a subset of $E_i$ which is algebraically free over $K$. Then $A_i \cap A_j = \varnothing$ for $i \neq j$ and $\bigcup_{i \in I} A_i$ is algebraically free over $K$.