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May 5, 2018 at 0:30 comment added Mike Battaglia Thank you Joel - I wonder, does any of this change if we use surjections rather than injections? I know that if two sets surject onto one another, this does not imply a bijection without AC. Still, suppose we simply declare that if A surjects onto B, this at least means A is "no smaller than" B. If A and B surject onto each other but there is no bijection, we could either just allow that to be the case, or we could even look at equivalence classes defined by having surjections both ways. Does anything like that lead to a neater picture, where the ordinals surject onto everything?
Apr 30, 2018 at 23:49 history edited Joel David Hamkins CC BY-SA 3.0
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Apr 30, 2018 at 23:29 vote accept Mike Battaglia
Apr 30, 2018 at 23:02 history answered Joel David Hamkins CC BY-SA 3.0