possible readings of "John seeks a bike or a fish"

What are the possible readings of the sentence
>John seeks a bike or a fish< in natural language?

Technically there are, I think, eight readings:
"to seek" being an intensional verb, both "bike" and "fish"
can be either intensional or extensional. Furthermore, the
disjunction can apply to either the speaker or John.
Let me paraphrase:

1. There are a bike and a fish, and John is trying to find
   one of these (he doesn't care which one).

2. There are a bike and a fish, and John is trying to find
   one of these (but I don't know which of the two he's
   actually looking for).

3. There is a bike, and John is trying to find either this
   bike or a (possibly non-existent) fish (he doesn't care...)

4. There is a bike, and John is trying to find either this
   bike or some fish (but I don't know...).

5. & 6. Similar to 3. & 4., but with the roles of "bike" and
	"fish" interchanged.

7. John is looking for a (possibly non-existent) bike or a
   (possibly non-existent) fish, and will be satisfied when
   he has found either one.

8. John is looking for a bike or a fish, both possibly non-
   existent, but I don't know which one he's looking for.

I hope this is clear.
This came up during a talk on quantification in natural
language. A theory thereof should account exactly for those
readings acceptable in natural language. But which ones are
in fact acceptable?

Koen.