By Su Gao
Presents effects from a truly lively sector of Research
Exploring an lively region of arithmetic that reports the complexity of equivalence kinfolk and class difficulties, Invariant Descriptive Set Theory offers an creation to the fundamental strategies, tools, and result of this idea. It brings jointly suggestions from a number of components of arithmetic, akin to algebra, topology, and common sense, that have assorted purposes to different fields.
After reviewing classical and potent descriptive set thought, the textual content reviews Polish teams and their activities. It then covers Borel reducibility effects on Borel, orbit, and common definable equivalence family members. the writer additionally offers proofs for various primary effects, reminiscent of the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. the subsequent half describes connections with the countable version thought of infinitary good judgment, in addition to Scott research and the isomorphism relation on usual periods of countable types, akin to graphs, timber, and teams. The booklet concludes with purposes to class difficulties and lots of benchmark equivalence family.
By illustrating the relevance of invariant descriptive set thought to different fields of arithmetic, this self-contained e-book encourages readers to additional discover this very lively zone of research.
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