Full Idea
There are sets of natural numbers definable in set-theory but not in arithmetic.
Gist of Idea
Some sets of natural numbers are definable in set-theory but not in arithmetic
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.123
Related Idea
Idea 13657 First-order arithmetic can't even represent basic number theory [Shapiro]