I'm reading Eliezer's posts about this, and how he says AIXI doesn't natively represent its own internal workings. But does this really matter? There are other ways to solve the anvil problem. Presumably, if the AIXI is embedded in the real world in some way (like, say, on a laptop) you can conceive that: it will eventually sense the laptop ("Hey, there is a laptop here, I wonder what it does!"), tamper with it a little bit, and then realize that whenever it tampers with it, some aspect of experience changes ("Hey, when I flip this bit on this strange laptop, I see blue! Weird!"). It would then make sense to hypothesize that this laptop is indeed itself. It would then infer that an anvil dropping on the laptop would destroy it, so it would try not to do that.

This process is perhaps similar to going through the whole of human science figuring out that our brains are ourselves. But going through all of human science is what it has do to solve a lot of other problems as well (like figure out dark matter, which we all agree it ought to be able to do).

Or, we could just start it up and tell it, "Hey, this laptop is you". I mean, kids have to be taught at some point that they think using their brains.