After we overview some of the known results on the descriptive
complexity approach to random 3-SAT, we present some new
results in this direction. In particular, we study sufficient
conditions that imply unsatisfiability of finite and infinite
3-CNF formulas, and obtain some non-expressibility results
for strong logics. Then we focus back to finite 3-CNF formulas
only, and study first-order definability on the typical 3-CNF. As
expected, the techniques differ significantly from the Datalog case.