 The ideas above can still be useful if we start with a sentence \(S\) that does say something either true or false without needing further interpretation. (Model theorists say that such a sentence is fully interpreted.) For example we can consider misinterpretations \(I\) of a fully interpreted sentence \(S\). A misinterpretation of \(S\) that makes it true is known as a nonstandard or unintended model of \(S\). The branch of mathematics called nonstandard analysis is based on nonstandard models of mathematical statements about the real or complex number systems; see  Section 4  below.