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Stationarity and elimination of imaginaries in stable and simple theories

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Types over real algebraically closed sets are shown to be stationary in stable theories, opening new pathways in model theory.
The proofs utilize general setups without specific field theories, emphasizing broader applicability of the findings.
Results by Delon, Messmer, and Wood indicate certain fields fail to eliminate imaginaries, impacting geometric considerations.
A general criterion derived from subgroup work reveals how geometric elimination fails, applying to both beautiful pairs and other structures.

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The study demonstrates that types over real algebraically closed sets are stationary, highlighting failures in elimination of imaginaries.

Charlotte Bartnick (2025) studied this question.

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The study demonstrates that types over real algebraically closed sets are stationary, highlighting failures in elimination of imaginaries.