The completeness of the isomorphism relation for countable boolean algebras

Transactions of the American Mathematical Society

Volumn 353, Issue 2, 2001, Pages 491-518

  Camerlo, Riccardo ^a   Cao, S U ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Borel rcducibility; Definable equivalence relations; Polish group actions; Separable boolean spaces

Indexed keywords

EID: 23044521948     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02659-3     Document Type: Article

References (22)

1. [An58] R. D. Anderson, The algebraic simplicity of certain groups of homeomorphisms, American Journal of Mathematics 80 (1958), 955-963. MR204607
2. [Ba75] J. Banvise, Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1975. MR5412519
3. [BK96] H. Bccker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Mathematical Society Lecture Notes Series 232, Cambridge University Press, 1996. MR98d54068
4. [B198] B. Blackadar, K-theory for Operator Algebras, Second Edition, Cambridge University Press, 1998. MR99g46104
5. [Br72] O. Bratteli, Inductive limits of finite dimensional C*-algebras, Transactions of the American Mathematical Society 171 (1972), 195-234. MR47844
6. [FS89] H. Friedman and L. Stanley, A Borel reducibility theory for classes of countable structures, The Journal of Symbolic Logic 54 (1989), 894-914. MR91f03062
7. [Ga98] S. Gao, The isomorphism relation between countable models and definable equivalence relations, PhD dissertation, UCLA, 1998.
8. [Go97] S. S. Goncharov, Countable Boolean Algebras and Decidability, Consultants Bureau, 1997. MR98h03044b
9. [Ha76] W. Hanf, Representing real numbers in denumerable Boolean algebras, Fundamenta Mathematicae 91 (1976), 167-170. MR547252
10. [Hj98] G. Hjorth, Classification and Orbit Equivalence Relations, Mathematical Surveys and Monographs, 75, Amer. Math. Soc., Providence, RI, 2000. CMP 200005
11. [HK95] G. Hjorth and A. S. Kechris, Analytic equivalence relations and Ulm type classifications, The Journal of Symbolic Logic 60 (1995), 1273-1300. MR96m54068
12. [Ho93] W. Hodges, Model Theory, Cambridge University Press, 1993. MR94e03002
13. [Iv91] P. Iverson, The number of countable isomorphism types of the theory of Boolean algebras, Colloquium Mathematicum 62 (2) (1991), 181-187. MR93a03038
14. [Kec95] A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, 1995. MR96e03057
15. [Kec98] A. S. Kechris, The descriptive classification of some classes of C-algebras, Proceedings * of the Sixth Asian Logic Conference (1998), 121-149.
16. [Ket78] J. Ketonen, The structure of countable Boolean algebras, Annals of Mathematics 108 (1978), 41-89. MR5810647
17. [Ko89] S. Koppelberg, Handbook of Boolean Algebras, vol. 1 (J.D. Monk ed.), North-Holland, 1989. MR90k06002
18. [Mu90] G. J. Murphy, C*-algebras and Operator Theory, Academic Press, 1990, MR91m46084
19. [Na72] M. A. Naimark, Normed Algebras, Wolters-Noordhoff, 1972. MR5511042
20. [Pa95] G. Panti, La logica infinito-valente di Lukasiewicz, PhD dissertation, Università degli studi di Siena, 1995.
21. [Pi89] R. S. Pierce, Countable Boolean algebras, in Handbook of Boolean Algebras (J. D. Monk and R. Bonnet eds.), Elsevier Science Publishers, 1989, 775-876. CMP 2110
22. [vM89] J. van Mill, Infinite Dimensional Topology. Prerequisites and Introduction, Elsevier Science Publishers, 1989. MR90a57025