mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the...

number. These are not the original axioms published by Peano, but are named in his honor. Some forms of the Peano axioms have 1 in place of 0. In ordinary...

arithmetic. Non-logical axioms may also be called "postulates", "assumptions" or "proper axioms". In most cases, a non-logical axiom is simply a formal logical...

Peano axioms (described below). In practice, not every proof is traced back to the axioms. At times, it is not even clear which collection of axioms a...

natural numbers represent 1 in various ways. In Giuseppe Peano's original formulation of the Peano axioms, a set of postulates to define the natural numbers...

induction axiom. In the context of the other Peano axioms, this is not the case, but in the context of other axioms, they are equivalent; specifically, the...

properties. In mathematical logic, the Peano axioms (or Peano postulates or Dedekind–Peano axioms), are axioms for the natural numbers presented in the...

axioms P* is defined in a language including the language of Peano arithmetic together with a new constant symbol x. The axioms consist of the axioms...

sets, and is the weakest known set theory whose theorems include the Peano axioms. The ontology of GST is identical to that of ZFC, and hence is thoroughly...