On Nov 3, 3:23 am, Herman Jurjus <hjm...@hetnet.nl> wrote: > On 11/3/2010 6:52 AM, herbzet wrote: > > What logically could exist -- that is, what is not inherently self- > > contradictory -- has mathematical existence. > Corollary: CH is false. > Proof: Since Cohen 1963 we know that it is logically consistent to > assume that there exists S, subset of P(N), equipollent neither to N nor > to P(N). > By your principle above, S mathematically exists. Therefore CH is false.
Corollary: CH is true. Proof: Since Goedel 1940 we know that it is logically consistent to assume that there exists f, a bijection between the set of countable ordinals (i.e., aleph_1) and P(N). By the principle above, f mathematically exists. Therefore CH is true. QED
(Note: The above "corollary" stems from an earlier sci.math discussion regarding the relationship between CH and Pen Maddy's "MAXIMIZE".)