Peano axioms
The intended interpretation is called the "standard model" (a term introduced by Abraham Robinson in 1960). In the context of Peano arithmetic, it consists of the natural numbers with their ordinary arithmetical operations. All models that are isomorphic to the one just given are also called standard; these models all satisfy the Peano axioms. There are also non-standard models of the (first-order version of the) Peano axioms, which contain elements not correlated with any natural number.