By Su Gao
Presents effects from a really energetic quarter of Research
Exploring an energetic zone of arithmetic that reports the complexity of equivalence kin and class difficulties, Invariant Descriptive Set Theory provides an advent to the elemental recommendations, tools, and result of this thought. It brings jointly recommendations from numerous components of arithmetic, akin to algebra, topology, and common sense, that have varied purposes 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 common definable equivalence kinfolk. the writer additionally offers proofs for various primary effects, resembling the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. the following half describes connections with the countable version conception of infinitary common sense, in addition to Scott research and the isomorphism relation on typical periods of countable versions, comparable to graphs, bushes, and teams. The ebook concludes with functions 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 ebook encourages readers to extra discover this very lively region of research.
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Invariant Descriptive Set Theory (Chapman & Hall/CRC Pure and Applied Mathematics) by Su Gao
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