Author:
Newelski Ludomir,Wencel Roman
Abstract
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.
Publisher
Cambridge University Press (CUP)
Cited by
9 articles.
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1. Convexity Relations and Generalizations of o-Minimality;Siberian Advances in Mathematics;2019-01
2. Definable sets in Stone algebras;Archive for Mathematical Logic;2016-05-31
3. Generalized o-minimality for partial orders;Siberian Advances in Mathematics;2013-01
4. Imaginaries in Boolean algebras;Mathematical Logic Quarterly;2012-04-18
5. Weak elimination of imaginaries for Boolean algebras;Annals of Pure and Applied Logic;2005-03