Full Idea
A single second-order sentence has second-order semantic consequences which are all and only the truths of arithmetic, but this is cold comfort because of incompleteness; no axiomatic system draws out the consequences of this axiom.
Gist of Idea
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically
Source
Theodore Sider (Logic for Philosophy [2010], 5.4.3)
Book Reference
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.124