"FredJeffries" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Jun 20, 10:46 am, "Julio Di Egidio" <ju...@diegidio.name> wrote: >> "WM" <mueck...@rz.fh-augsburg.de> wrote in message >> news:email@example.com... >> > On 20 Jun., 15:33, "Julio Di Egidio" <ju...@diegidio.name> wrote: >> >> >> >> (E.g. did anybody study the latter construction [the L=[0,L]]? Does >> >> the "issue" exists at all, >> >> > This issue does not exist in any forum or journal where matheologians >> > are the dominating fraction. >> >> If that distinction has any merit, then it's hard to believe that nobody >> has >> looked into it yet. Anyway, if that is so, this "issue" might very well >> become the basis for my PhD thesis... so to speak. > > I cannot find your original question. From the few comments I have read > it seems that you wish to abolish limit ordinals and relabel the successor > of a limit ordinal to the limit ordinal's label, etc. Thus, your omega is > what > is currently called omega + 1, your omega + 1 is what is now referred to > as omega + 1, omega + omega for you would be (omega + omega + 1)... > > Is that close? > > Is there some problem you believe you can solve with such a system?
Now consider this alternative definition: each ordinal is the well-ordered set of all non-strictly smaller ordinals. In symbols, lambda = [0, ambda]. -- I.e. the set includes the ordinal to which it corresponds.
That's what I am asking about, the second definition: if it works, if it exists in the literature, etc.
By the way, thanks very much for the references you give in the other post.