Full Idea
Given any series which is endless, contains no repetitions, has a beginning, and has no terms that cannot be reached from the beginning in a finite number of steps, we have a set of terms verifying Peano's axioms.
Gist of Idea
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], I)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.8