sentences:  Because any two transitive models of set theory with the same ordinals have the same constructible universe, Shoenfield's theorem shows that two such models must agree about the truth of all formula_1 sentences.One consequence of Shoenfield's theorem relates to the axiom of choice.Gödel proved that the constructible universe "L" always satisfies ZFC, including the axiom of choice, even when "V" is only assumed to satisfy ZF.