Does oversized pipe avoid venting requirements?

I'm building my own summer place with slab on grade costruction and concrete walls. The only fixture on an outside wall (concrete) is the kitchen sink, which is also on the concrete slab. It is 18 feet from the 4" horizontal main. I'm under the UPC and the local county does not allow AAVs. They suggested that I cast the vent pipe into the concrete wall, but that's easier said than done. I'm thinking of proposing an island vent, but even that is a little difficult because of tying the vent leg into the horizontal and into a stack vent. Each of the horizontal drain and vent pipes would have to be dug into the underslab material (with a pick axe), and then backfilled.

So, I was wondering if it was possible to increase the size of the kitchen drain pipe such that no vent was required and I would need to dig just one trench (I have plenty of drop between the sink and the main). What if a 2 inch drain pipe went through the slab into a 3" elbow with 3" pipe all the way to the 4" main? It seems a little crazy that it would need to be vented, but my question is, is there a pipe size that would allow just one pipe going to the main without a vent?

Mark

Is there a pipe size that would allow just one pipe going to the main without a vent?

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No. There are cases where something comes off the horizontal from an oversized pipe, Sometimes a shower from a lav line sized at 2" that's because you have vented the lav, and th lav vent may also vent the shower, but you need the vertical vent in there for the kitchen, as you would on the lav vent too.

If your building department is telling you to cast a vent in the concrete, then that is how it is.

Plumbing doesn't change because you use it in the Summer.
Plumbing doesn't know seasons.
Whenever I travel to third world countries, I'm so glad we have tight plumbing codes here.
When I was in Guatemala, I tried to fix some kitchen sink plumbing to get rid of the smell. I had no luck with it.
It was horrible, all the time.
I don't think the venting was right on that one either.

Run the pipe on the inside of the wall and paint it the same color as the wall. Burying it in concrete just makes it harder to fix.