Peano’s axioms can be stated as follows: 1. Zero is a number. 2. The immediate successor of a number is a number. 3. Zero is not the immediate successor of a number. 4. No two numbers have the same immediate successor. 5. Any property belonging to zero, and also to the immediate successor of every number that has the property, belongs to all numbers. The last axiom formulates what is often called the “principle of mathematical induction.”
Interesting, I have come across similar axioms in the "Principia Mathematics" by Whitehead & Russell. Of course, I haven't read the original text (apparently Godel has read it cover-to-cover, no wonder he was able to tatter it into pieces)
