As that appears to be your main soil stack as there is a wye showing under the floor above, as GReynolds929 said, you need a separate vent. And you should indeed use a wye to connect to the 4". However, I would suggest using a 4x4x2 wye.
there is likely some sort of vent manifold in the top story. You'd tie your vent line there.
what is concerning to some plumbers is the fact that if this soilstack clogs up, the backed up water goes into the kitchen sink.