Complete analytic equivalence relations

作者: Alain Louveau , Christian Rosendal

DOI: 10.1090/S0002-9947-05-04005-5

关键词: Pure mathematicsEquivalence relationClass (set theory)MathematicsGlobal analytic functionMathematical proofBorel equivalence relationDiscrete mathematicsModel theory

摘要: We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e. maximum the Borel reducibility ordering. The proofs use some general results concerning wider class of quasi-orders.

参考文章(24)
Lee J. Stanley, Borel Diagonalization and Abstract Set Theory: Recent Results of Harvey Friedman Studies in logic and the foundations of mathematics. ,vol. 117, pp. 11- 86 ,(1985) , 10.1016/S0049-237X(09)70155-7
Alain Louveau, On the reducibility order between borel equivalence relations Studies in logic and the foundations of mathematics. ,vol. 134, pp. 151- 155 ,(1995) , 10.1016/S0049-237X(06)80042-X
Richard Mansfield, Galen Weitkamp, Recursive Aspects of Descriptive Set Theory ,(1985)
Mikhael Gromov, Misha Katz, Pierre Pansu, Stephen Semmes, None, Metric Structures for Riemannian and Non-Riemannian Spaces ,(1999)
Greg Hjorth, Universal co-analytic sets Proceedings of the American Mathematical Society. ,vol. 124, pp. 3867- 3873 ,(1996) , 10.1090/S0002-9939-96-03494-6
Alexander S. Kechris, Howard Paul Becker, The descriptive set theory of Polish group actions ,(1996)
Alexander S. Kechris, Actions of Polish Groups and Classification Problems Cambridge University Press. ,(2003)
Riccardo Camerlo, Su Gao, The completeness of the isomorphism relation for countable Boolean algebras Transactions of the American Mathematical Society. ,vol. 353, pp. 491- 518 ,(2000) , 10.1090/S0002-9947-00-02659-3