On Nov 3, 4:50 pm, Transfer Principle <lwal...@lausd.net> wrote: > 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".)
We have concluded that a consequence of herbzet's idea is that there are systems in which CH is true and systems in which CH is false.