On ordered structures, a decision problem is FO($\le$, PFP) definable if and only if it is SO(TC) definable, that is, in PSPACE: the capture of polynomial space by partial fixed points, due to Abiteboul and Vianu. A partial iteration is a deterministic walk on the assignments of its own block, which gives one direction. Conversely, a partial fixed point iterates the deterministic machine problem complete for PSPACE: it loads the initial configuration, takes the unique step while there is one, and stutters on accepting or stuck configurations, so that a halting run is a converging iteration; every problem of PSPACE pulls that definition back along its reduction to the machine problem.