Interpolative fusions

We define the interpolative fusion T-boolean OR* of a family (T-i)(i is an element of I) of first-order theories over a common reduct T-boolean AND, a notion that generalizes many examples of random or generic structures in the model-theoretic literature. When each T-i is model-complete, T-boolean OR* coincides with the model companion of T-boolean OR = boolean OR T-i is an element of I (i). By obtaining sufficient conditions for the existence of T-boolean OR*, we develop new tools to show that theories of interest have model companions.

Automated summary

By defining the interpolative fusion T-boolean OR*, we generalize many examples of random or generic structures in the model-theoretic literature and develop new tools to show that theories of interest have model companions.