4 ms·

Can you elaborate on this / provide further reading?

• praptak 5y ago
  Wikipedia page on Peano axioms maybe. Edit/elaborate: First order rules like "no element X has successor(X)=0" and "two distinct elements have two distinct successors" assure there is a chain of successors that starts with zero and does not cycle into itself. This however does not mean that every model is isomorphic to the natural numbers because a cycle of elements separate from this chain does not falsify any of the rules(axioms). So you need an additional rule to stipulate that every element of the set is reachable from zero. To express this you have to go outside first order logic.