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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DOI 10.2307/2694978
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References found in this work BETA
Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.

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Citations of this work BETA
Weak Elimination of Imaginaries for Boolean Algebras.Roman Wencel - 2005 - Annals of Pure and Applied Logic 132 (2-3):247-270.
Imaginaries in Boolean Algebras.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (3):217-235.

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