[FOM] An axiom to settle the continuum hypothesis ?
Adib Ben Jebara
adib.jebara at topnet.tn
Wed Mar 21 00:07:58 EDT 2007
An axiom to settle the continuum hypothesis ?
Paul Cohen used a set of generic reals to prove the consistency of the
negation of the continuum hypothesis with other axioms.
It is my opinion that such sets do not really exist for a Platonist.
My opinion is that the continuum hypothesis is true.
Here is a tentative axiom from me to try to prove it. Axiom : An infinite
subset of the power set of N has a bijection either with a countable union
of (pair wise disjoint) sets of n elements or with a countable Cartesian
products of (pair wise disjoint) sets of n elements.
Mr Andreas Blass proved that this axiom is equivalent to the continuum
hypothesis.
So, the axiom is consistent with the other usual axioms and independent from
them, from the works of Kurt Godel and Paul Cohen, respectively.
Mr Andreas Blass used the assumption that the Cartesian product is not the
empty set but he did not use the axiom of choice.
Regards,
Adib Ben Jebara.
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