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Infinite set, disjunction, and tautology

  1. Apr 18, 2010 #1
    Let {A1, A2, A3, ... } be an in finite set of formulas in propositional logic. Assume that
    for every valuation v there is some n (depending on v) such that v(An) = 1. Show
    then that there is some fixed m with A1 [tex]\vee[/tex] A2 [tex]\vee[/tex] ... [tex]\vee[/tex] Am a tautology.

    This is equivalent to showing that v(Ai) = 1 for at least one 1[tex]\leq[/tex]i[tex]\leq[/tex]m. But I'm not sure where to proceed from here.
     
  2. jcsd
  3. Apr 19, 2010 #2
    Start by considering the set [itex]\left\{A_1,A_1\vee A_2,A_1\vee A_2 \vee A_3\cdots\right\}[/itex] and assume that none of its elements is a tautology. Note also that any valuation may be identified with an infinite binary sequence.
     
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