Full Idea
The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof.
Gist of Idea
No two numbers having the same successor relies on the Axiom of Infinity
Source
Alan Musgrave (Logicism Revisited [1977], §4 n)
Book Reference
-: 'British Soc for the Philosophy of Science' [-], p.112
A Reaction
[He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical.