| Sumario: | Let ${\cal S}$ be a Scott set, or even an <italic>ω</italic>-model of WWKL. Then for each <italic>A</italic> ε <italic>S</italic>, either there is <italic>X</italic> ε <italic>S</italic> that is weakly 2-random relative to <italic>A</italic>, or there is <italic>X</italic> ε <italic>S</italic> that is 1-generic relative to <italic>A</italic>. It follows that if <italic>A</italic>,…,<italic>A</italic> ε <italic>S</italic> are noncomputable, there is <italic>X</italic> ε <italic>S</italic> such that each <italic>A</italic> is Turing incomparable with <italic>X</italic>, answering a question of Kučera and Slaman. More generally, any ∀∃ sentence in the language of partial orders that holds in ${\cal D}$ also holds in ${{\cal D}^{\cal S}}$ , where ${{\cal D}^{\cal S}}$ is the partial order of Turing degrees of elements of ${\cal S}$.
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