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.
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Mathematics Subject Classification (2000): Primary 03C15, Secondary 03C35, 06E05
Revised version: 2 February 2004
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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
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DOI: https://doi.org/10.1007/s001530000069