 Transfer immediately implies that any uniquely definable object (defined without reference to standardness) is in fact a standard object. So the empty set is standard, \(\omega\) is standard, and so forth. But it is not the case that all elements of standard objects are standard. For consider the cardinality of a finite set containing all standard objects; this is clearly greater that any standard natural number (usual element of \(\omega)\) yet it is equally clearly an element of \(\omega\). It turns out to be provable that every set all of whose elements are standard is a standard finite set.