Unformatted text preview: G . Assume that G is a graph with inﬁnitely many vertices V = { x 1 ,x 2 ,x 3 ,... } . Show that if every ﬁnite subgraph of G has a coloring with k colors, then G has a coloring with k colors. (30%) 3 * . Let { A 1 ,A 2 ,A 3 ,... } be an inﬁnite set of formulas in propositional logic. Assume that for every valuation v there is some n (depending on v ) such that v ( A n ) = 1. Show then that there is some ﬁxed m with A 1 ∨ A 2 ∨ ··· ∨ A m a tautology. 1...
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This note was uploaded on 07/19/2010 for the course MA 6 taught by Professor Inessaepstein during the Spring '09 term at Caltech.
 Spring '09
 InessaEpstein
 Math

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