Re: Review of Mueckenheims book.

On 10 Mrz., 02:44, "William Hughes" <wpihug...@xxxxxxxxxxx> wrote:
On Mar 9, 12:38 pm, mueck...@xxxxxxxxxxxxxxxxx wrote:

<snip>



In order to obtain the answer to the question
whether there is any infinite path in the union of all finite trees
(which is the same as the question whether there is any infinite line
in the union of all finite lines of the EIT)

No. Lines go across, columns go down, paths go down.

If you have problems of visualizing, please turn the tree by 90 degree
in positive direction. That does not change its structure.

The question
"is there any infinite
path in the union of all finite trees?"

Yes. And the paths are projected so that the WM shows their length
(not their number).

is the same as the question
"is there any infinite column in the EIT?".

How would it be possible to find out by a projection whether there is
an ifinite column? The WM of a column is just this column. If you
project the sixth column, then you get the WM = 6. The We can only
tell us about the enities which are projected rectanguarly, i.e, from
the side. Remember: The WM of the *lines* is < aleph_0. Now put the
finite paths in the positions of the lines.


Since the EIT contains an infinite number of lines, the answer is yes.

That answer is the same as: There are infinitely many finite paths.

Regards, WM

.

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