 Characterization of the standard model of arithmetic in L(ω1,ω). Here the standard model of arithmetic is the structure N = ⟨N, +, ·, s, 0⟩, where N is the set of natural numbers, +, ·, and 0 have their usual meanings, and s is the successor operation. Let  L  be the first-order language appropriate for N. Then the class of  L-structures  isomorphic to N coincides with the class of models of the conjunction of the following  L(ω1,ω) sentences (where 0 is a name of 0):