Re: Mathematicians are in deep *** for 2 reasons

suber says a consequence of skolems paradox is

*This means that there simply are no sets whose cardinality is absolutely
uncountable.

but this contradicts set theory and guts it

for

the cardinality of the reals MUST really be uncountable in all the models
of the system

suber points out

This strange situation is not hypothetical. There are systems of set
theory (or number theory or predicate logic) that contain a theorem which
asserts in the intended interpretation that the cardinality of the real
numbers exceeds the cardinality of the naturals. That's good, because it's
true. Such systems therefore say that the cardinality of the reals is
uncountable.


So the cardinality of the reals MUST really be uncountable in all the
models of the system




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