CSPs over FO expansions of finitely bounded homogeneous model-complete cores are either FO-definable (in non-uniform AC0) or L-hard under FO reductions.
On the relational width of first-order expansions of finitely bounded homogeneous binary cores with bounded strict width
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Constraint Satisfaction Problems over Finitely Bounded Homogeneous Structures: a Dichotomy between FO and L-hard
CSPs over FO expansions of finitely bounded homogeneous model-complete cores are either FO-definable (in non-uniform AC0) or L-hard under FO reductions.