Generalising Hrushovski’s fusion technique we construct the free fusion of two strongly minimal theories T₁,T₂ intersecting in a totally categorical sub-theory T₀. We show that if, e.g., T₀ is the theory of infinite vector spaces over a finite field then the fusion theory Tω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of Tω, proving that if both T₁, T₂ are 1-based then, Tω can be collapsed into a strongly minimal theory, if some additional technical conditions hold—all trivially satisfied if T₀ is the theory of infinite vector spaces over a finite field 𝔽q.
"Fusion over sublanguages." J. Symbolic Logic 71 (2) 361 - 398, June 2006. https://doi.org/10.2178/jsl/1146620149