Definable sets in Boolean-ordered o-minimal structures. I

Journal of Symbolic Logic 66 (4):1821-1836 (2001)
Abstract
We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures
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    Roman Wencel (2012). Imaginaries in Boolean Algebras. Mathematical Logic Quarterly 58 (3):217-235.
    Roman Wencel (2005). Weak Elimination of Imaginaries for Boolean Algebras. Annals of Pure and Applied Logic 132 (2-3):247-270.
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