Invariant Descriptive Set Theory (Chapman & Hall/CRC Pure - download pdf or read online

By Su Gao

Presents effects from a really lively quarter of Research

Exploring an energetic quarter of arithmetic that reviews the complexity of equivalence kin and category difficulties, Invariant Descriptive Set Theory provides an creation to the elemental innovations, tools, and result of this conception. It brings jointly innovations from a variety of parts of arithmetic, resembling algebra, topology, and common sense, that have various functions to different fields.

After reviewing classical and potent descriptive set idea, the textual content reports Polish teams and their activities. It then covers Borel reducibility effects on Borel, orbit, and normal definable equivalence relatives. the writer additionally presents proofs for varied basic effects, similar to the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. the subsequent half describes connections with the countable version conception of infinitary good judgment, besides Scott research and the isomorphism relation on ordinary sessions of countable versions, akin to graphs, timber, and teams. The ebook concludes with purposes to class difficulties and lots of benchmark equivalence relatives.

By illustrating the relevance of invariant descriptive set idea to different fields of arithmetic, this self-contained e-book encourages readers to extra discover this very energetic sector of research.

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