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Math Help - First-order formulae for b is greater than or equal to a.

  1. #1
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    First-order formula for b is greater than or equal to a.

    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 \beta(x,y) such that for any
    a,b\in\mathbb{R}, R\models\beta(a,b) if and only if b\geq{a}.

    Is this correct (i think that it is but im just a little unsure)

    a=b\vee (\exists{y}(y\neq0\wedge\exists{x}(x.x=y))\wedge a+y=b)

    thanks for any help
    Last edited by hmmmm; July 5th 2011 at 08:33 AM.
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  2. #2
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    Re: First-order formula for b is greater than or equal to a.

    Yes, this would work.
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