Full Idea
The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity.
Gist of Idea
Many concepts can only be expressed by second-order logic
Source
George Boolos (On Second-Order Logic [1975], p.48)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.521