Abstract
Let G = (V,E) be a graph on the well ordered set V which has no infinite path. If the order type of V, tpV, is a limit ordinal less than w w+21 , then there is a subset Vā ā V having the order type (under the induced ordering) which is an independent set. If tpV = w w+21 , then this statement is independent of the axioms of set theory.
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Milner, E.C. (1990). Ordered Graphs Without Infinite Paths. In: Hahn, G., Sabidussi, G., Woodrow, R.E. (eds) Cycles and Rays. NATO ASI Series, vol 301. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0517-7_14
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DOI: https://doi.org/10.1007/978-94-009-0517-7_14
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