I guess if we don’t have choice and R isn’t well-orderable than I guess omega_1 could be just incomparable to it for all I know.
That’s how I remember it, although I don’t know a reference (much less a proof). All we know is that omega_1 is not larger than R.
That’s how I remember it, although I don’t know a reference (much less a proof). All we know is that omega_1 is not larger than R.