As the Wikipedia page alludes, Egan, and this book in particular, was surely the inspiration for Tegmark's Mathematical Universe Hypothesis; the notion that all logically/mathematically consistent structures exist on some level, our universe among them.

(Though in truth the Pythagoreans of 2500 BC -- those adherents to what can rightly be called the first universalizing European religion -- believed much the same thing. Egan and the Pythagoreans, but not Tegmark, also considered the nature of time in such a scenario; eternal recurrence was a Pythagorean idea.)

For that matter, all inconsistent structures ought to also "exist" — they're just indistinguishably boring, for inconsistency leads to triviality?

Everything that you can imagine, no matter how trivial, is a consistent notion that can be expressed mathematically as a true logical proposition. This includes an empty room, a Platonic solid, physical entropy, whatever. As Wittgenstein once noted, "logically consistent statements which are a priori true are possibilities which ensure their own truth."

What stands in opposition to this? The logically nonsensical – the incomputable. This includes anything discrete that can't be simulated, even in principle. These things cannot exist even in an infinite mathematical universe; for everything in such a universe is emergent, but such things cannot emerge.

Isn’t that referred to as the Dust Theory?

I just finished Permutation City for the first time since it’s come up on HN a few times so I thought I’d give it a read. (Mild spoiler alert) I found that once everything was in the autoverse I stopped caring about the characters’ copies. Maybe that’s an intended perspective, or maybe it says something about me.