Hostname: page-component-5cf477f64f-r2nwp Total loading time: 0 Render date: 2025-04-04T02:24:47.066Z Has data issue: false hasContentIssue false
  • English
  • Français

A remark on Martin's Conjecture

Published online by Cambridge University Press:  12 March 2014

Su Gao
Su Gao*
Affiliation:
Department of Mathematics, California Institute of Techology, Pasadena, CA 91125, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that the strong Martin conjecture is false. The counterexample is the first-order theory of infinite atomic Boolean algebras. We show that for this class of Boolean algebras, the classification of their (ω + ω)-elementary theories can be reduced to the classification of the elementary theories of their quotient algrbras modulo the Frechét ideals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 401 - 406
Copyright
Copyright © Association for Symbolic Logic 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[H]Hodges, W., Model theory, Cambridge University Press, Cambridge, 1993.CrossRefGoogle Scholar
[I]Iverson, P., The number of countable isomorphism type of complete extensions of the theory of Boolean algebras, Colloquium Mathematicum, Polish Academy of Sciences, vol. 62, (1991), pp. 181–187.CrossRefGoogle Scholar
[K]Koppelberg, S., Handbook of Boolean Algrbras, vol. 1, North-Holland, Amsterdam-New York, 1989, volums I–III edited by Monk, J. D. and Bonnet, R..Google Scholar
[W]Wagner, C. M., On Martin's conjecture, Annals of Mathematical Logic, vol. 22 (1982), pp. 47–67.CrossRefGoogle Scholar