[FOM] A question about a new definition of Cardinality.

Zuhair Abdul Ghafoor Al-Johar zaljohar at yahoo.com
Wed Jan 18 12:19:50 EST 2012

Dear FOMers,

Cardinality is a one place function satisfying the following
basic property.

for all x, for all y: Cardinality(x) = Cardinality(y) iff  x bijective to y

Now Let C(x) be the set of all sets hereditarily subnumerous to
P(P(x)) that are equinumerous to x.

Is there a known model of ZF in which C does not satisfy the above
basic property?

Best Regards


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