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Feb 18, 2012 at 11:44 comment added Jirka Hanika Reals always have an uncountable subset (uncountable inside the universe), supposing we are talking within $ZF$ or similar. I supposed that Ramiro was asking, what if $pR$ were somehow banned from stepping on $pN$'s candidate values, to which he received a perfect answer. Or am I just missing a more specialized topic/axiomatics here?
Feb 7, 2012 at 8:45 comment added Dávid Natingga Thank you for your answer, together with the comments of François G. Dorais, it is clearer to me, however I have not thought yet of other universes like Ramiro de la Vega mentioned which may be worth exploring.
Feb 7, 2012 at 8:42 vote accept Dávid Natingga
Feb 6, 2012 at 9:43 history answered Jirka Hanika CC BY-SA 3.0