Polish group actions: Dichotomies and generalized elementary embeddings

DOI10.1090/S0894-0347-98-00258-6zbMath0894.03027OpenAlexW1658875765MaRDI QIDQ4383175

Howard Becker

Publication date: 24 March 1998

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-98-00258-6

zbMATH Keywords

descriptive set theorydichotomy theoremsPolish group actioncli groupelementary embedding of orbits

Mathematics Subject Classification ID

Transformation groups and semigroups (topological aspects) (54H15) Descriptive set theory (03E15) General groups of measure-preserving transformations (28D15) Model theory of denumerable and separable structures (03C15)

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Cites Work

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• On Lusin's restricted continuum problem
• A proof of Vaught's conjecture for \(\omega\)-stable theories
• Descriptive set theory
• Set theory. An introduction to independence proofs
• Topology and descriptive set theory
• On disjoint Borel uniformizations
• Orbit cardinals: On the effective cardinalities arising as quotient spaces of the form \(X/G\) where \(G\) acts on a Polish space \(X\)
• Transformation groups and \(C^ *\)-algebras
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• A Borel reductibility theory for classes of countable structures
• Structure and order structure in Abelian groups
• Counting the number of equivalence classes of Borel and coanalytic equivalence relations
• On Martin's conjecture
• Dual Et Quasi-Dual D'Une Algebre de Banach Involutive
• A Glimm-Effros Dichotomy for Borel Equivalence Relations
• Analytic determinacy and 0^#
• Equivalences Generated by Families of Borel Sets
• Forcing with tagged trees
• The Invariant ∏ 0 α Separation Principle
• On automorphism groups of countable structures
• Vaught’s conjecture and the Glimm-Effros property for Polish transformation groups
• Polish Group Actions and the Vaught Conjecture
• The topological Vaught's conjecture and minimal counterexamples
• Equivalence Relations Induced by Actions of Polish Groups
• Orbits of denumerable models of complete theories
• The classification of hypersmooth Borel equivalence relations
• Locally Compact Transformation Groups