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In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This collection of survey papers by leading researchers covers a wide variety of recent developments in these subjects and their interconnections. Researchers and graduate students interested in either of these areas will find this volume to be an excellent introduction to problems and research directions arising from their interconnections.

The authors present some surprising connections that sets of uniqueness for trigonometic series have with descriptive set theory. They present many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. Topics covered include symmetric perfect sets and the solution to the Borel Basis Problem for U, the class of sets of uniqueness. To make the material accessible to both logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as...