Reverse mathematics and infinite traceable graphs

Mathematical Logic Quarterly 58 (1-2):18-28 (2012)
Abstract
We analyze three applications of Ramsey’s Theorem for 4-tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey’s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA0
Keywords traceable graphs  03D80  lattice theory. MSC (2010) 03B30  effective combinatorics  05C63  Reverse mathematics
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DOI 10.1002/malq.201020066
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