Abstract.
For a complete first order theory of Boolean algebras T which has 
nonisomorphic countable models, we determine the first limit ordinal α = α(T) such that 
We show that for some 
and for all other T‘s, 
A nonprincipal ideal I of B is almost principal, if 
a is a principal ideal of B} is a maximal ideal of B. We show that the theory of Boolean algebras with an almost principal ideal has 
complete extensions and characterize them by invariants similar to the Tarski’s invariants.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gao, S.: A remark on Martin’s conjecture, J. Symbolic Logic 66 (2001), 401–406
Hodges, W.: Model Theory, Cambridge University Press, (1993)
Iverson, P.: The number of countable isomorphism types of complete extensions of the theory of Boolean algebras, Colloquium Mathematicum 62, 181–187 (1991)
Keisler, H.J.: Model Theory for infinitary Logic, North Holland, (1971)
Koppelberg, S.: Handbook of Boolean algebras Vol. 1, Edited by J.D. Monk, North Holland (1989)
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): Primary 03C15, Secondary 03C35, 06E05
Revised version: 2 February 2004
Rights and permissions
About this article
Cite this article
Rubin, M. On Lα,ω complete extensions of complete theories of Boolean algebras. Arch. Math. Logic 43, 571–582 (2004). https://doi.org/10.1007/s001530000069
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s001530000069