The Farah conjecture on random twins of unstable theories

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Let TT be a first-order countable unstable theory. Two models MM and NN of TT are random twins if they are non-isomorphic but become isomorphic after the universe is extended by adding a random real. The Farah conjecture. There are non-isomorphic models M,NM,N of TT which are random twins. The conjecture asks whether every first-order countable unstable theory has such a pair of models; the supplied text gives no indication that this has been proved or refuted.

References

Primary source

Saharon Shelah, “Twins: non-isomorphic models forced to be isomorphic. Part I”, arXiv:2505.02088 (2025).

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