Finite thickness

In formal language theory, a class of languages $\mathcal L$ has finite thickness if for every string s, there are only finitely many consistent languages in $\mathcal L$. This condition was introduced by Dana Angluin in connection with learning, as a sufficient condition for language identification in the limit. The related notion of M-finite thickness

We say that $\mathcal L$ satisfies the MEF-condition if for each string s and each consistent language L in the class, there is a minimal consistent language in $\mathcal L$, which is a sublanguage of L. Symmetrically, we say that $\mathcal L$ satisfies the MFF-condition if for every string s there are only finitely many minimal consistent languages in $\mathcal L$. Finally, $\mathcal L$ is said to have M-finite thickness if it satisfies both the MEF and MFF conditions.

Finite thickness implies M-finite thickness. However, there are classes that are of M-finite thickness but not of finite thickness (for example, let {L_n} be a class of languages such that $L_0 \subseteq L_1 \subseteq \ldots$).