A dichotomy theorem for mono-unary algebras
Gao, Su
Fundamenta Mathematicae, Tome 163 (2000), p. 25-37 / Harvested from The Polish Digital Mathematics Library
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We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212427 
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     title = {A dichotomy theorem for mono-unary algebras},
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     volume = {163},
     year = {2000},
     pages = {25-37},
     zbl = {0955.03049},
     language = {en},
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Gao, Su. A dichotomy theorem for mono-unary algebras. Fundamenta Mathematicae, Tome 163 (2000) pp. 25-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p25bwm/

[00000] [Ba] J. Barwise, Admissible Sets and Structures: an Approach to Definability Theory, Perspectives in Math. Logic, Springer, Berlin, 1975. | Zbl 0316.02047

[00001] [BK] H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge Univ. Press, Cambridge, 1996. | Zbl 0949.54052

[00002] [FS] H. Friedman and L. Stanley, A Borel reducibility theory for classes of countable structures, J. Symbolic Logic 54 (1989), 894-914. | Zbl 0692.03022

[00003] [Ga] S. Gao, The isomorphism relation between countable models and definable equivalence relations, Ph.D. dissertation, UCLA, 1998.

[00004] [HKL] L. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928. | Zbl 0778.28011

[00005] [HK] G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm-type classifications, J. Symbolic Logic 60 (1995), 1273-1300. | Zbl 0847.03023

[00006] [Ma] L. Marcus, The number of countable models of a theory of one unary function, Fund. Math. 58 (1980), 171-181. | Zbl 0363.02055

[00007] [Sa] R. Sami, Polish group actions and the Vaught Conjecture, Trans. Amer. Math. Soc. 341 (1994), 335-353. | Zbl 0795.03069

[00008] [St] J. R. Steel, On Vaught's Conjecture, in: Cabal Seminar 76-77, Lecture Notes in Math. 689, Springer, Berlin, 1978, 193-208.