By Su Gao

ISBN-10: 1584887931

ISBN-13: 9781584887935

Presents effects from a truly lively zone of Research

Exploring an lively zone of arithmetic that reviews the complexity of equivalence family members and category difficulties, Invariant Descriptive Set Theory provides an advent to the fundamental strategies, equipment, and result of this thought. It brings jointly concepts from a variety of components of arithmetic, reminiscent of algebra, topology, and good judgment, that have varied functions to different fields.

After reviewing classical and powerful descriptive set thought, the textual content reports Polish teams and their activities. It then covers Borel reducibility effects on Borel, orbit, and common definable equivalence relatives. the writer additionally offers proofs for varied basic effects, akin to the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. the subsequent half describes connections with the countable version concept of infinitary common sense, in addition to Scott research and the isomorphism relation on normal sessions of countable types, comparable to graphs, bushes, and teams. The booklet concludes with purposes to category difficulties and lots of benchmark equivalence family.

By illustrating the relevance of invariant descriptive set concept to different fields of arithmetic, this self-contained booklet encourages readers to extra discover this very energetic quarter of research.

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Invariant Descriptive Set Theory (Chapman & Hall/CRC Pure and Applied Mathematics) by Su Gao

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