In mathematical logic, independence refers to the unprovability of a sentence from other sentences. A sentence s is independent of a given first-order theory T if T neither proves nor refutes s; that is, it is impossible to prove s from T, and it is also impossible to prove from T that s is false. Sometimes, s is said (synonymously) to be undecidable from T; this is not the same meaning of "decidability" as in a decision problem.