Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Simple complete Boolean algebras

Authors: Thomas Jech and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 129 (2001), 543-549
MSC (1991): Primary 03Exx
Published electronically: July 27, 2000
MathSciNet review: 1707521
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For every regular cardinal $\kappa $ there exists a simple complete Boolean algebra with $\kappa $ generators.

References [Enhancements On Off] (What's this?)

  • 1. M. Bekkali and R. Bonnet, Rigid Boolean Algebras, in: ``Handbook of Boolean Algebras'' vol. 2 (J. D. Monk and R. Bonnet, eds.,) p. 637-678, Elsevier Sci. Publ. 1989. CMP 21:10
  • 2. T. Jech, A propos d'algèbres de Boole rigide et minimal, C. R. Acad. Sc. Paris, série A, 274 (1972), 371-372. MR 44:6569
  • 3. T. Jech, Simple complete Boolean algebras, Israel J. Math. 18 (1974), 1-10. MR 50:4300
  • 4. T. Jech and S. Shelah, A complete Boolean algebra that has no proper atomless complete subalgebra, J. of Algebra 182 (1996), 748-755. MR 97j:03109
  • 5. R. B. Jensen, Definable sets of minimal degree, in: Mathematical logic and foundations of set theory. (Y. Bar-Hillel, ed.) p. 122-128, North-Holland Publ. Co. 1970. MR 46:5130
  • 6. A. Kanamori, Perfect set forcing for uncountable cardinals, Annals Math. Logic 19 (1980), 97-114. MR 82i:03061
  • 7. K. McAloon, Consistency results about ordinal definability, Annals Math. Logic 2 (1970), 449-467. MR 45:1753
  • 8. K. McAloon, Les algèbres de Boole rigides et minimales, C. R. Acad. Sc. Paris, série A 272 (1971), 89-91. MR 42:7491
  • 9. G. Sacks, Forcing with perfect closed sets, in: ``Axiomatic set theory,'' (D. Scott, ed.) Proc. Symp. Pure Math. 13 (1), pp. 331-355, AMS 1971. MR 43:1827
  • 10. S. Shelah, Why there are many nonisomorphic models for unsuperstable theories, in: Proc. Inter. Congr. Math., Vancouver, vol. 1, (1974) pp. 259-263. MR 54:10008

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03Exx

Retrieve articles in all journals with MSC (1991): 03Exx

Additional Information

Thomas Jech
Affiliation: Department of Mathematics, The Pennsylvania State University, 218 McAllister Bldg., University Park, Pennsylvania 16802
Address at time of publication: Center for Theoretical Study, Jilská 1, 110 00 Praha 1, Czech Republic

Saharon Shelah
Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel

Received by editor(s): January 13, 1999
Received by editor(s) in revised form: April 30, 1999
Published electronically: July 27, 2000
Additional Notes: The authors were supported in part by National Science Foundation grants DMS–98-02783 and DMS–97-04477.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society