```Date: Dec 28, 2012 12:14 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Distinguishability of paths of the Infinite Binary tree???

On 27 Dez., 19:04, Zuhair <zaljo...@gmail.com> wrote:> On Dec 27, 3:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>> > Here is a parameter free enumeration of all finite initial segments of> > the paths of the Binary Tree:>> > 0> > 1, 2> > 3, 4, 5, 6> > 7, ...>> > Regards, WM>> Show me a parameter free formula "phi(y)" where the alleged> enumeration you've just depicted above is defined after i.e. suppose> your enumeration is denoted as "En" then show me that: For all y. y in> En iff phi(y).> Remember parameter free formula phi(y) means a formula in which ONLY y> occurs free. If you show that then I'd agree with you. If you don't> show that, then you didn't prove that your alleged enumeration is> parameter free. AND please spare me any responses that gives a> different definition for the term "parameter free definable" that you> have in your mind since simply it is not relevant to the "parameter> free definable" concept that I'm speaking about.It not obvious to me, what you call parameter-free. (And you need notexplain it, because I am not interested in your interpretation.) Butit is obvious to me that Cantor enumerated the rational numbers justlike I enumerate the finite paths of the Binary Tree. And heenumerated the digits of the diagonal in just the same way, namelyassuming the complete existence of all natural numbers.Regards, WM
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