Elimination of imaginaries for generic derivations

Let TT be an algebraically bounded theory, and let Tgδˉ,?T^{\bar \delta,?}_g be its theory of generic derivations. Elimination of imaginaries modulo TeqT^{eq} means that imaginaries in the expansion are controlled up to the imaginaries already present in TeqT^{eq}. Elimination-of-imaginaries conjecture. Tgδˉ,?T^{\bar \delta,?}_g has elimination of imaginaries modulo TeqT^{eq}. In particular, if TT has geometric elimination of imaginaries (GEI), then Tgδˉ,?T^{\bar \delta,?}_g also has GEI, and if TT has EI, then Tgδˉ,?T^{\bar \delta,?}_g also has EI. This extends elimination-of-imaginaries properties from algebraically bounded theories to their generic-derivation expansions; the source provides no resolution.

Sources & referencesView supporting material

Primary source

Fornasiero Antongiulio and Terzo Giuseppina, “Generic derivations on algebraically bounded structures II. Model theoretical properties”, arXiv:2507.22181 (2026).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.