L, deterministic logarithmic space, is the class of decision problems definable in first-order logic with a deterministic transitive closure, which captures it on ordered structures by a theorem of Immerman. Hardness is the cofinal hardness of the NP core, under relativized ordered first-order reductions, and coL is the class of problems whose complement is in L. L-completeness is membership together with L-hardness. No machine enters the definition.