 The complement of \(T\), the set of false sentences \(F\), is not a theory even in this technical sense. Since falsehoods always entail truths, \(F\) is not closed under the consequence relation. (This may be the reason why we have no expression like the Falsth: the set of false sentences does not describe a possible alternative to the actual world.) But \(F\) too is a perfectly good set of sentences. The consequences of any theory \(A\) that can be formulated in \(L\) will thus divide between \(T\) and \(F\). Popper called the intersection of \(A\) and \(T\), the truth content of \(A\) (\(A_T\)), and the intersection of \(A\) and \(F\), the falsity content of \(A\) (\(A_T\)). Any theory \(A\) is thus the union of its non-overlapping truth content and falsity content. Note that since every theory entails all logical truths, these will constitute a special set, at the center of \(T\), which will be included in every theory, whether true or false.