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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 finite 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.

M-finite thickness should be compared with finite thickness. While finite thickness implies the existence of a mind change bound, M-finite thickness does not. For example, let \{L_n\} be a class of languages such that L_0 \subseteq L_1 \subseteq \ldots then there is no mind change bound for this class.