 The members of \(U\) are called standard sets, or standard objects; those in \(^*U - U\) nonstandard sets or nonstandard objects: \(^*U\) thus consists of both standard and nonstandard objects. The members of \(^*U\) will also be referred to as *-sets or *-objects Since \(U \subseteq ^*U\), under this convention every set (object) is also a *-set (object) The \(^*\)-members of a *-set \(A\) are the *-objects \(x\) for which \(x \mathbin{^*{\in}} A\).