 Since we have formula_1, the first-order reductions are weaker reductions than the logspace reductions.Many important complexity classes are closed under first-order reductions, and many of the traditional complete problems are first-order complete as well (Immerman 1999 p. 49-50).For example, ST-connectivity is FO-complete for NL, and NL is closed under FO reductions (Immerman 1999, p. 51) (as are P, NP, and most other "well-behaved" classes).