Borel separability of the coanalytic Ramsey sets

Annals of Pure and Applied Logic 144 (1-3):130-132 (2006)
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Let AC and AI denote the collections of graphs with vertex set ω and which have, respectively, no infinite independent subgraph, and no infinite complete subgraph. Both AC and AI are coanalytic sets of reals that are not analytic, and they are disjoint by Ramsey’s theorem. We prove that there exists a Borel set separating AC and AI, and we discuss the sense in which this is an infinite analogue of a weak version of



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