Results 1 to 3 of 3

Math Help - Notation: "infinity" superscript on universal quantifier

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Nederland
    Posts
    4

    Notation: "infinity" superscript on universal quantifier

    Hey guys,

    I've come across a some notation that I have not seen before and since it's all symbols, I couldn't really find anything on Google about it. I don't think it's necessary/relevant to explain the entire context here, but the formula read like this:

    P(e) \rightarrow (\forall^{\infty}y)(f(e,y) \in COINF)

    where COINF if the index set of all coinfinite recursively enumerable sets.

    It's probably not all that complicated, but I've never seen the \forall^{\infty} quantifier notation before. What does it mean? The variable y is supposed to range over the natural numbers.

    Thank you!
    Selinde
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: Notation: "infinity" superscript on universal quantifier

    I know what recursively enumerable sets are, but I don't think \forall^\infty is a universally accepted notation. I believe it should have been defined earlier in your text. If it were \exists^\infty, it could mean that there exist infinitely many objects. Maybe \forall^\infty y means "for all y's that are indices of infinite recursively enumerable sets"? If your text is available online, I could look into it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2013
    From
    Nederland
    Posts
    4

    Re: Notation: "infinity" superscript on universal quantifier

    The text is available here: http://arxiv.org/pdf/1302.7069v1.pdf -- the notation first occurs on the bottom of page 8 and is not defined earlier. That's why I assumed I was just missing some knowledge (as is usually the case when I'm reading these things ) The meaning that you suggested is a possibility, but I do not yet understand the proof enough to check this.



    Edit: I think it might mean "for all but finitely many", could this be correct?
    Last edited by Selinde; March 28th 2013 at 09:55 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. the quantifier "there exist uncountably many"
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: December 17th 2011, 03:37 PM
  2. Replies: 0
    Last Post: May 8th 2011, 01:54 PM
  3. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  4. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  5. "Universal" gas constant(/s)
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: May 7th 2009, 08:16 PM

Search Tags


/mathhelpforum @mathhelpforum