> Of course, when one simply works within a system of axioms, the > problem is obscured by the presupposition of denotation. It merely > hides itself in set theory as the question of a well-ordering for > the reals.
Of course.I've omitted the fact that it's often helpful to have a standard representation in telling when things are different. However , in general, proving they are the same is more problematic . Deciding whether two real number-generating algorithms are equal in general implies solving the halting problem . In a completeness sense, decision is still possible . However, comparing arbitrary sets of real numbers becomes less clear.
I'm intrigued .How does denotation relate to the well ordering (or lack thereof ) of the reals? Can you offer references?