By Greg Hjorth

Activities of Polish teams are ubiquitous in arithmetic. In definite branches of ergodic conception and practical research, one reveals a scientific examine of the gang of measure-preserving alterations and the unitary workforce. In good judgment, the research of countable versions intertwines with effects about the activities of the endless symmetric crew. this article develops the speculation of Polish staff activities totally from scratch, eventually offering a coherent concept of the ensuing orbit equivalence sessions that can permit entire class via invariants of an indicated shape. The booklet concludes with a criterion for an orbit equivalence relation classifiable by means of countable constructions thought of as much as isomorphism. This self-contained quantity deals an entire remedy of this energetic quarter of present learn and develops a tricky normal idea classifying a category of mathematical items as much as a few correct inspiration of isomorphism or equivalence. Greg Hjorth bought the Carol Karp Prize for striking paintings on turbulence and countable Borel equivalence kin from the organization of Symbolic good judgment.

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