Syntactic nonstandard analysis requires a great deal of care in applying the principle of set formation (formally known as the axiom of comprehension), which mathematicians usually take for granted. As Nelson points out, a fallacy in reasoning in IST is that of "illegal set formation". For instance, there is no set in IST whose elements are precisely the standard integers (here "standard" is understood in the sense of the new predicate). To avoid illegal set formation, one must only use predicates of ZFC to define subsets.