I think you are confusing the object-level and the meta-level (and incidentally confusing everyone who doesn't know advanced set theory). In any case, if you w

I think you are confusing the object-level and the meta-level (and incidentally confusing everyone who doesn't know advanced set theory). In any case, if you want to talk about the computable reals, then call them computable reals. Don't say "reals" for "computable reals", even if you think the former don't exist. Unicorns don't exist either, but that doesn't justify defining "unicorn" as "a horse".