In my original formulation, each $K[i]$ contains the result of a CylindricalDecomposition call with variables $\{x,y,z\}$.

Thus, the problem with my RegionPlot above is that fixing $z=i$ passes two variables ( $x$ and $y$) and a constant ( $z=i$) to a CylindricalDecomposition expecting three variables. This yields error messages like "1 is not a valid variable".

Here is a MWE for a solution:

arg1[x_, y_, z_] := {x >= y && y >= z && z >= 0}
RegionPlot3D[Evaluate[CylindricalDecomposition[arg1[x, y, z], {x, y, z}]], {x, 0, 2}, {y, 0, 2}, {z, 0, 2}]
RegionPlot[Evaluate[CylindricalDecomposition[arg1[x, y, 0], {x, y}]], {x, 0, 2}, {y, 0, 2}]