Given a language L and an indexed class C = { L1, L2, L3, ... } of languages, a member language Lj ∈ C is called a minimal concept of L within C if L ⊆ Lj, but not L ⊊ Li ⊆ Lj for any Li ∈ C.[{{cite book|author1=Andris Ambainis |author2=Sanjay Jain |author3=Arun Sharma | chapter=Ordinal mind change complexity of language identification| title=Computational Learning Theory| year=1997| volume=1208| pages=301–315| publisher=Springer| series=LNCS| url=https://www.comp.nus.edu.sg/~sanjay/paps/efs2.pdf}}; here: Definition 25]
The class C is said to satisfy the MEF-condition if every finite subset D of a member language Li ∈ C has a minimal concept Lj ⊆ Li. Symmetrically, C is said to satisfy the MFF-condition if every nonempty finite set D has at most finitely many minimal concepts in C. Finally, C is said to have M-finite thickness if it satisfies both the MEF- and the MFF-condition.
[Ambainis et al. 1997, Definition 26]
Finite thickness implies M-finite thickness.[Ambainis et al. 1997, Corollary 29] However, there are classes that are of M-finite thickness but not of finite thickness (for example, any class of languages C = { L1, L2, L3, ... } such that L1 ⊆ L2 ⊆ L3 ⊆ ...).