Fusion over sublanguages

Assaf Hasson, Martin Hils
2006 Journal of Symbolic Logic (JSL)  
Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T 1. T 2 intersecting in a totally categorical sub-theory T 0. We show that if. e.g., T 0 is the theory of infinite vector spaces over a finite field then the fusion theory T ω, exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of T ω, proving that if both T 1, T 2 are 1-based then. Tω can be collapsed into a strongly minimal theory, if some additional
more » ... cal conditions hold—all trivially satisfied if T 0 is the theory of infinite vector spaces over a finite field .
doi:10.2178/jsl/1146620149 fatcat:jutbivtmtjhshfseq7ihny3uxa