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Math Help - Fol 1

  1. #1
    Junior Member
    Joined
    Nov 2011
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    Fol 1

    Show that

    \{\forall x(\alpha \rightarrow \beta), \forall x \alpha \} \models \forall x \beta .

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    We show that any structure A for the language and any function s: V \rightarrow |A| that satisfies \{\forall x(\alpha \rightarrow \beta), \forall x \alpha \} also satisfies \forall x \beta, where s denotes a function from the set V of all variables into the universe |A| of A. For any d \in |A|, we have \models_A(\alpha \rightarrow \beta)[s(x|d)] and \models_A \alpha [s(x|d)].
    It follows that \models_A \beta [s(x|d)]. which in turn implies that \models_A \forall x \beta [s].

    Is this proof O.K or am I missing something?

    Thank you.
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  2. #2
    MHF Contributor
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    Re: Fol 1

    Yes, this proof is OK.
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