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Math Help - representability of functions, math logic

  1. #1
    Junior Member
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    representability of functions, math logic

    Any help with this question would be great, thanks.

    Show that if S and T are representable sets of numbers then so are;

    S intersection T
    S union T
    N-S (where N are the natural numbers)
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  2. #2
    MHF Contributor
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    When will you people learn to post relevant details? Logic is a subject notorious for having multiple ways of defining the same concepts.

    I assume that a set S is by definition representable when there is a formula F(x) in the language of Peano arithmetic such that for every natural number n, n is in S iff F(n) is true in the standard model (the usual natural numbers).

    If this is the case, the answer is trivial: take conjunction, disjunction and negation and the formulas that represent S and T.
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