CH yet again.

Robert E. Beaudoin wrote:

| [AD implies] that every uncountable set of reals has a perfect subset
| (and hence is in one-one correspondence with the continuum).

| this implies ... that there can be no "explicit" example
| of a set of reals "defying CH".

This had been my first thought too, but I think Keith Ramsay is
quite right with his response:

But a set could serve as an example of what he asked for
even if there is some conjecture like AD that implies it's
a continuum or countable, as long as that conjecture is necessary
for the proof that it's a continuum or countable.

IOW, there might well be an explicit set of reals given, that might be
noncontinuum uncountable, and that the latter fact was an implicant
for not-AD.

Probably it's still not what Bill was hoping to get, but I think he
just has to learn to accept slightly more exotic objects than
he's used to dealing with.

Well I'm pretty sure by this time that no "simple" example is ever
going to appear out of the woodwork!

Still, your injunction to become more familar with L or 0# is too
much for me, alas. Regarding L, I have been trying to grok it
for many years now; I can follow the definition OK, but as soon as
I try to "understand" it, I find myself at sea - I just cannot
connect it to anything familiar in set theory, or see how it
"feels" in itself or what consequences it might possibly have.
It seems to be some fault in my psychological make-up, sadly.

And as for 0#, I cannot even get to the point where someone
could present me with a definition! I seem to have reached
the limits of my understanding of abstract objects with these.

So maybe I should re-address my whole query to:- does anyone
have any bon mots or advice on how I might increase my understanding
of these two things?

-------------------------------------------------------------------------
Bill Taylor W.Taylor@xxxxxxxxxxxxxxxxxxxxx
-------------------------------------------------------------------------
In science one tries to tell people,so as to be understood by everyone,
something noone ever knew before.In literature it's the exact opposite.
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Relevant Pages

  • Re: CH yet again.
    ... | [AD implies] that every uncountable set of reals has a perfect subset ... | of a set of reals "defying CH". ... a continuum or countable, as long as that conjecture is necessary ...
    (sci.logic)
  • Re: Why real numbers and points cant model continuum
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    (sci.math)
  • Re: The Numerical and the Intuitive Continuum
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  • Re: Why real numbers and points cant model continuum
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    (sci.math)
  • Re: Interval in a continuum is a fractal
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