Abstract:We investigate the chromatic number of innite graphs whose denition is motivated by the theorem of Engelking and Karªowicz (in [3]). In these graphs, the vertices are subsets of an ordinal, and two subsets X and Y are connected i for some a ∈ X ∩ Y the order-type of a ∩ X is dierent from that of a ∩ Y .In addition to the chromatic number χ(G) of these graphs we study χ κ (G), the κ-chromatic number, which is the least cardinal µ with a decomposition of the vertices into µ classes none of which contains a κ-com… Show more
“…Theorem 5.1 (Engelking and Kar lowicz [EK65], see also [AY08]). Assume χ <θ = χ, δ < (2 χ ) + an ordinal and A α α<δ a sequence of sets of size ≤ χ.…”
Section: A Methods To Construct Nice Iteration Candidatesmentioning
Using a finite support iteration of ccc forcings, we construct a model of ℵ1 < add(N ) < cov(N ) < b < non(M) < cov(M) = c.2010 Mathematics Subject Classification. 03E17, 03E35, 03E40.
“…Theorem 5.1 (Engelking and Kar lowicz [EK65], see also [AY08]). Assume χ <θ = χ, δ < (2 χ ) + an ordinal and A α α<δ a sequence of sets of size ≤ χ.…”
Section: A Methods To Construct Nice Iteration Candidatesmentioning
Using a finite support iteration of ccc forcings, we construct a model of ℵ1 < add(N ) < cov(N ) < b < non(M) < cov(M) = c.2010 Mathematics Subject Classification. 03E17, 03E35, 03E40.
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