 Characterization of well-orderings in L(ω1,ω1). The base language  L  here includes a binary predicate symbol ≤. Let σ1 be the usual  L-sentence  characterizing linear orderings. Then the class of  L-structures  in which the interpretation of ≤ is a well-ordering coincides with the class of models of the  L(ω1,ω1) sentence σ = σ1  ∧ σ2, where