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Math Help - underlying set

  1. #1
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    underlying set

    let Phi_n denote the sentence for all x_1 for all x_2 ...for all x_{n-1} there exists x_n (neg (x_{n} =x_1) ) /\ neg (x_{n} =x_2) /\.../\
    neg(x_{n} = x_{n-1} ).
    how can I show that every model of Phi_n must have at least n elements in the underlying set .
    Last edited by Mike12; March 26th 2011 at 02:19 PM.
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  2. #2
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    If a model has fewer than n elements, then you can instantiate x_1, ..., x_{n-1} with all of these elements (possibly, with repetition). Then you can't find x_n that is different from all of x_1, ..., x_{n-1}.
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  3. #3
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    Thanks alot emakarov
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