Single Idea 10833

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order]

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