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Recursively enumerable language with infinite alphabet

  1. Nov 18, 2008 #1
    Is an infinite language with an infinite alphabet always recursively enumerable?
    Last edited: Nov 18, 2008
  2. jcsd
  3. Nov 18, 2008 #2
    isn't it just enumerable?
  4. Nov 19, 2008 #3
    What's "enumerable"?
  5. Nov 19, 2008 #4
    countablely infinate
  6. Nov 19, 2008 #5


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    Last edited: Nov 19, 2008
  7. Nov 19, 2008 #6
    So.... no? Interesting.
  8. Nov 19, 2008 #7


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    If the language has uncountable alphabet, surely not?
  9. Nov 20, 2008 #8
    I was thinking that since the alphabet is infinite (countable or not), a Turing machine would need infinitely many states to recognize it, which goes against the definition of a TM.
  10. Nov 20, 2008 #9
    Isn't everything, should you accept the axiom of choice? I guess you meant it in the constructable sense.
  11. Nov 21, 2008 #10
    What does the axiom of choice have to do with anything?
  12. Nov 21, 2008 #11
    Ah, my mistake. See, I was thinking in the lines of the well ordering theorem. But the theorem doesn't state anything about every element of set having a predecessor, so it doesn't necessarily equate denumerability. I knew this was weird.
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