regular languages. Finite thickness A class of languages has finite thickness if every non-empty set of strings is contained in at most finitely many languages of the class. This is exactly Condition 3 in Angluin's paper. Angluin showed that if a class of recursive languages has finite thickness, then it is learnable in the limit. A class with finite thickness certainly satisfies MEF-condition and MFF-condition; in other words, finite thickness implies M-finite thickness. Finite elasticity A class of languages is said to have finite elasticity if for every infinite sequence of strings and every infinite sequence of languages in the class , there exists a finite number n such that implies is inconsistent with . It is shown that a class of recursively enumerable languages is learnable in the limit if it has finite elasticity. Mind change bound A bound over the number of hypothesis changes that occur before convergence. Other concepts Infinite cross property A language L has infinite cross property within a class of languages if there is an infinite sequence of distinct languages in and a sequence of finite subset such that: , , , and . Note that L is not necessarily a member of the class of language. It is not hard to see that if there is a language with infinite cross property within a class of languages, then that class of languages has infinite elasticity. Relations between concepts Finite thickness implies finite elasticity; the converse is not true. Finite elasticity and conservatively learnable implies the existence of a mind change bound. Finite elasticity and M-finite thickness implies the existence of a mind change bound. However, M-finite thickness alone does not imply the existence of a mind change bound; neither does the existence of a mind change bound imply M-finite thickness. Existence of a mind change bound implies learnability; the converse is not true. If we allow for noncomputable learners, then finite elasticity implies the existence of a mind change bound; the converse is not true. If there is no accumulation order for a class of languages, then there is a language (not necessarily in the class) that has infinite cross property within the class, which in turn implies infinite elasticity of the class. Open questions If a countable class of recursive languages has a mind change bound for noncomputable learners, does the class also have a mind change bound for computable learners, or