Slicing the Truth

[2][3] These chapters also review some of the tools needed in this study, including computability theory, forcing, and the low basis theorem.

[4] Chapter six, "the real heart of the book",[2] applies this method to an infinitary form of Ramsey's theorem: every edge coloring of a countably infinite complete graph or complete uniform hypergraph, using finitely many colors, contains a monochromatic infinite induced subgraph.

However, as David Seetapun originally proved, the version of the theorem for graphs is weaker than ACA0, and it turns out to be inequivalent to any one of the big five subsystems.

[2] And reviewer Benedict Eastaugh calls it "a welcome addition ... providing a fresh and accessible look at a central aspect of contemporary reverse mathematical research.

[3] Reviewer Jeffry Hirst suggests Computability Theory by Rebecca Weber as a good source for the background needed to read this book.