Bruno, do we have an agreed-upon identification "what" to call an observer? I may heve missed it on the list, if yes. Your post below speaks about the topic, but I don't see some conclusion: is it the unformalizable first person concept, is it upon formal, or nonformal considerations? Is the essence of an 'observer' unresolved and so hard to involve it in activities for conclusions?
I mean a short, concise plain language identification.
OK, from the UDA and its arithmetical translation, an (atomic) physical observable yes-no proposition
is "just" a true arithmetical sigma_1 sentence ( i. e. with the shape "it exists a number n such that P(n)" with F(n) decidable (= UD accessible), explicitely provable (= true in all consistent extensions) and
explicitely true in at least one consistent extension. If you "quantize" p by <>p, that is sum up on the world where you survive (comp immortality) you get the "measure 1" logic. It remains open exactly which sort of quantum logic we get.
The "sensible observer" is the same + the truth of p.
Let me summarize the theaetetical variants, understanding could come later :)
1) Independently of comp (!)
The scientific discourse = p The first person discourse = p & p The observer discourse = p & <>p The sensible observer disc. = p & <>p & p
This gives 4 logics (G, S4Grz, Z, X), x 2, because of G/G* distinction, minus 1, because
S4Grz* = S4Grz. 7 logics.
2) with comp you must add the axiom p -> p (= the modal form of the arithmetical UD accessibility, I call it "1" for sigma_1: indeed EnP(n) -> EnP(n))
That gives 8 new logics: G1, S4Grz1, Z1, X1, G1*, S4Grz1*, Z1*, X1*
Minus 1, because I conjecture (S4Grz+ p->p)* = S4Grz+ p->p.
In my (non-physics) verbalizing I tried lately to identify an observer with something receiving (maybe responding to) any topically relatable information (not the 'bit' of course).
Very close to my "cop-out" for consciousness of a decade ago.
Don't hesitate to remind links or to summarize in a post.