  Another result which holds in the first-order case but fails  for  L(κ,ω) with κ ≥ ω1 (and also for  L(ω1,ω1), although this is more difficult to prove) is the prenex normal form theorem. A sentence is prenex if all its quantifiers appear at the front; we give an example of an  L(ω1,ω)-sentence which is not equivalent to a conjunction of prenex sentences. Let  L  be the first-order language without extralogical symbols and let σ be the  L(ω1,ω)-sentence which characterizes the class of finite sets. Suppose that σ were equivalent to a conjunction