[FOM] Intuitionism, predicativism, and ill-defined domains

[Hendrik Boom]

On Thu, Oct 27, 2005 at 12:58:56AM -0500, Nik Weaver wrote:
> 
> To give another example, predicativists have some difficulty
> with assertions of the form "such-and-such a recursive ordering
> of omega is a well-ordering" (meaning, to be precise, there are
> no proper progressive subsets --- we must be specific because
> there are several classically equivalent versions of the concept
> of well-ordering which are not predicatively equivalent).

I'd very much like to see a short list of these inequivalent versions
of well-ordering.  I gather three of them are

  -- every subset has a least element
  -- strong induction works (is this the same as the one you used
     just now?  Or is there a subtle distinction?)
  -- every descending sequence terminates

Which one is generally considered to be the paroper
constructive/predicative/intuitionistic one?  Or do
constructivists, predicativists, and intuitionists
not agree on this?

-- hendrik