Let {A1, A2, A3, ... } be an infinite set of formulas in propositional logic. Assume that(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Infinite set, disjunction, and tautology

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