Re: Continuum hypothesis

On Aug 16, 10:25 am, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:
On Thu, 16 Aug 2007 djr...@xxxxxxxxxx wrote:



On Aug 16, 7:33 am, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:
On Wed, 15 Aug 2007 djr...@xxxxxxxxxx wrote:
OK, I was reading a paper by Woodin on CH and he said something to the
effect that whether one adopts CH or ?CH does not affect the
arithmetic statements true in the theory. I took this to mean
"arithmetic" statements as statements which quantify over numbers, or
sets of numbers, and so on. i.e. statements of any order number
theory.

What does ?CH meant? 'not CH' sometimes written '~CH'?
What is an arithmetic statement? A statement of FOL
with Peano's axioms included as also appropiate function
(successor) and predicate (is natural number) symbols?- Hide quoted text -

- Show quoted text -

Yeah it means not CH, screwy keyboard. What is an arithmetic
statement? Well that was what I was wondering. I guessed he (Woodin)
meant a statement of number theory of some order, first order or
second order or whatever. Then if it makes sense to say CH is not a
statement of any order number theory, then what he said would make
sense.


.