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In 'Elementary pairs of models' by Bouscaren, she mentions with a remark at the end that if $T$ is a superstable theory then $T$ has a Vaughtian pair if and only if $T^\text{eq}$ has a Vaughtian pair, a fact which is proven in her preprint 'A note on Vaughtian pairs'. She also mentions that this is sharp in that Ziegler has constructed examples of strictly stable theories with no Vaughtian pairs, but which do have imaginary Vaughtian pairs.

I cannot track down either of these references. Can anyone replicate either of these arguments? I'm primarily interested in the statement that a superstable theory with no Vaughtian pairs has no imaginary Vaughtian pairs. The $\omega$-stable case follows easily from the Baldwin-Lachlan theorem, but I can't see how to do the strictly superstable case.

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  • $\begingroup$ If you email Elisabeth, I'm sure she'd be happy to give you more information, or share the preprint with you if it still exists. $\endgroup$ Commented Jan 14, 2019 at 0:20

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