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Math Help - Difine a first order formula for positive numbers

  1. #1
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    Difine a first order formula for positive numbers

    Let \mathcal{V}_{ar}={+,.,0,1} be the vocabulary of arithmetic. Let R be the structure that has universe \mathbb{R} and interprets the vocabulary in the usual manner.

    Define a \mathcal{V}_{ar} formula \alpha(x) such that for any
    a\in\mathbb{R}, R\models\alpha(a) if and only if a is positive.

    Im sure I really should be able to do this but I cannot think how to.

    Thanks for any help

    For clarity R is the structure and \mathbb{R} is the real numbers.

    (what is the LaTex for the reals?)

    Thanks again
    Last edited by hmmmm; July 5th 2011 at 02:36 AM.
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  2. #2
    MHF Contributor
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    Re: Difine a first order formula for positive numbers

    How about a\ne0\land\exists x\,x\cdot x=a?
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  3. #3
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    Re: Difine a first order formula for positive numbers

    haha yeah thanks I was thinking about that for ages!
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