Unexpected region from RegionPlot3D[ ]?

Why isn’t this surface colored or even displayed as a surface? Is RegionPlot3D the wrong function to use? I’m just beginning to experiment with plotting sets of points.

This is very curious too:

RegionPlot3D[
 Abs[x - y] < 1 && y > 0, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
 PlotPoints -> 6, AxesLabel -> Automatic]