 Note that the necessary truth of \(a = b\) does not imply the necessary existence of objects \(a\) or \(b\). We may assume that what a rigid term \(a\) denotes at a possible world (or moment of time) \(w\) need not exist in \(w\). Secondly, we do not ordinarily say things of the form “\(x\) is the same as \(y\)”. Instead, we say “\(x\) and \(y\) are the same person” or “\(x\) and \(y\) are the same book”. The standard view is that the identity component of such statements is just ‘\(x\) is the same as \(y\)’. For example, according to the standard view, ‘\(x\) and \(y\) are the same person’ reduces to ‘\(x\) and \(y\) are persons and \(x\) is the same as \(y\)’, where the second conjunct may be formalized as in FOL\(^=\).