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Ordered algebraic structures --- Ordered algebraic structures. --- Structures algébriques ordonnées. --- Betweenness relations (Mathematics) --- Automorphisms. --- Automorphismes. --- Permutation groups. --- Groupes de permutations. --- Automorphisms --- Permutation groups --- Substitution groups --- Group theory --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- B-sets --- Between relations (Mathematics) --- Betweenness (Mathematics) --- Intermediacy (Mathematics) --- Relations of between (Mathematics) --- Relations of betweenness (Mathematics) --- Relations related to betweenness (Mathematics) --- Set theory --- Symmetry (Mathematics)

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Set theory --- Descriptive set theory --- Forcing (Model theory) --- Borel sets --- B-measurable sets --- B-sets --- Borel-measurable sets --- Borel subsets --- Borelian sets --- Subsets, Borel --- Analytic sets --- Topology --- Model theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Borel sets.

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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.

Set theory. --- Forcing (Model theory) --- Borel sets. --- B-measurable sets --- B-sets --- Borel-measurable sets --- Borel subsets --- Borelian sets --- Subsets, Borel --- Analytic sets --- Topology --- Model theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics

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Borel sets --- Ergodic theory --- Measure theory --- Rigidity (Geometry) --- Set theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Geometric rigidity --- Rigidity theorem --- Discrete geometry --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Transformations (Mathematics) --- B-measurable sets --- B-sets --- Borel-measurable sets --- Borel subsets --- Borelian sets --- Subsets, Borel --- Analytic sets --- Topology --- Mathematical logic --- Ergodic theory. Information theory --- Measure theory. Mathematical integration