Theory of Relations

The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey''s theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver''s embeddability theorem for scattered chains, using Nash-Williams'' better quasi-orderings, barriers and forerunning.The second part (chapters 9 to 12) extends to...