Kitchen sink s-trap

Here's the plumbing under the kitchen sink. I plan on adding a dishwasher, but before I connected it to the drain I thought I'd read up a bit on plumbing. Well, I just learned that S-traps aren't code.
The house was built in 1922, and it's two stories.

Here's under the sink, and where it goes down into the basement.






Any suggestions on improving the situation?
I don't see a way to add a p-trap, so I guess my real question is there a best way to do an s-trap?
Many thanks.

At the least the s trap needs to be removed, they can siphon and let sewer gas into your home. If no venting is available you could check if an AAV is allowed in your area. I would also remove the flex line from the sink. The connection in the basment is incorrect as well, it should be a y into the main line.

Thanks for the info. AAV's aren't allowed where I am and no venting is available...

The connection to the main line is fine.
A horizontal waste line can dump into a santee that is on the vertical anywhere in the US.
You should at least remove the funny accordion piping, and install a Studor or AAV vent for the kitchen sink.

Good to hear about the main line connection.
AAV's aren't code in Illinois and they aren't sold locally.
We've only lived here a couple months but we haven't noticed any sewer gas smell with the existing setup.