 Intuitively, the idea is that \(F\) is hereditary in the R-series if \(F\) is always ‘passed along’ from \(x\) to \(y\) whenever \(x\) and \(y\) are a pair of R-related objects. (We warn the reader here that the notation ‘\(\mathit{Her}(F,R)\)’ is merely an abbreviation of a much longer statement. It is not a formula of our language having the form ‘\(R(x,y)\)’. In what follows, we sometimes introduce other such abbreviations.)