Full Idea
Categoricity cannot be attained in a first-order language.
Gist of Idea
Categoricity can't be reached in a first-order language
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 7.3)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.196
Related Ideas
Idea 10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
Idea 13636 An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro]