Includes bibliographies.

Dilators, generalized Goodstein sequences, independence results: a survey ; Some uses of dilators in combinatorial problems. I ; Cross products of Souslin trees ; Ergodic Ramsey theory ; Ultrafilters related to Hindman's finiteunions theorem and its extensions ; Logical analysis of some theorems of combinatorics and topological dynamics ; A remark on partition relations for infinite ordinals with an application to finite combinatorics ; A summary of "On Ramseytype theorems and their provability in weak formal systems" ; Provably computable functions and the fast growing hierarchy ; Rigid Borel sets and better quasiorder theory ; Some problems on finite and infinite graphs ; The metamathematics of the graph minor theorem ; Summable ultrafilters and finite sums ; On undecidability of the weakened Kruskal theorem ; Well quasiorderings, long games and a combinatorial study of undecidability ; On the theory of quasiordinal diagrams ; Improved bounds to the length of proofs of finitistic consistency statements ; Nonstandard universes with strong embeddings, and their finite approximations ; Unprovable theorems and fastgrowing functions V Michele Abrusci ; V M Abrusci JY Girard and J Van de Wiele ; Bruce Ackman and Jim Owings ; Vitaly Bergelson ; Andreas Blass ; Andreas R Blass Jeffry L Hirst and Stephen G Simpson ; J E Baumgartner and A Hajnal ; Stephen H Brackin ; Wilfried Buchholz and Stan Wainer ; Fons van Engelen Arnold W Miller and John Steel ; P Erdos ; Harvey Friedman Neil Robertson and Paul Seymour ; Neil Hindman ; Martin Loebl and Jiri Matousek ; Jaroslav Nesetril and Robin Thomas ; Mitsuhiro Okada and Gaisi Takeuti ; P Pudlak ; JP Ressayre ; Stephen G Simpson