[FOM] Cardinality in the absence of AC
Timothy Y. Chow
tchow at math.princeton.edu
Fri Jun 7 13:37:28 EDT 2019
I wrote:
> can we construct sets A and B such that
>
> 1. in ZFC we can prove that |A| = |B|, but
> 2. in ZF+LM we can prove that B outnumbers A?
On Fri, 7 Jun 2019, Floris van Doorn wrote:
> You can take
> A = { X in powerset(R) | X is not Lebesgue measurable }
> B = powerset(R)
Good point! So I guess my real question is a vaguer one---are there
examples that violate one's intuition about cardinality, the way the R vs.
R/Q example violates one's intuition?
Tim
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