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  1.  4
    Weakly o-Minimal Nonvaluational Structures.Roman Wencel - 2008 - Annals of Pure and Applied Logic 154 (3):139-162.
    A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of o-minimal expansions of (...)
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  2.  9
    On the Strong Cell Decomposition Property for Weakly o‐Minimal Structures.Roman Wencel - 2013 - Mathematical Logic Quarterly 59 (6):452-470.
  3.  11
    Topological Properties of Sets Definable in Weakly o-Minimal Structures.Roman Wencel - 2010 - Journal of Symbolic Logic 75 (3):841-867.
    The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets (...)
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  4. Small Theories of Boolean Ordered o-Minimal Structures.Roman Wencel - 2002 - Journal of Symbolic Logic 67 (4):1385-1390.
    We investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are $\aleph_{0}-categorical$ . We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.
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  5. Definable Sets in Boolean Ordered o-Minimal Structures. II.Roman Wencel - 2003 - Journal of Symbolic Logic 68 (1):35-51.
    Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal theories are essentially bidefinable (...)
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  6.  18
    Definable Sets in Boolean-Ordered o-Minimal Structures. I.Ludomir Newelski & Roman Wencel - 2001 - Journal of Symbolic Logic 66 (4):1821-1836.
    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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  7.  4
    Weak Elimination of Imaginaries for Boolean Algebras.Roman Wencel - 2005 - Annals of Pure and Applied Logic 132 (2-3):247-270.
    We give a complete characterization of Boolean algebras admitting weak elimination of imaginaries in terms of elementary invariants.
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  8.  38
    Groups, Group Actions and Fields Definable in First‐Order Topological Structures.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (6):449-467.
    Given a group , G⊆Mm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V⊆G and define a new topology τ on G with which becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory facts concerning (...)
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  9.  12
    Imaginaries in Boolean Algebras.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (3):217-235.
    Given an infinite Boolean algebra B, we find a natural class of equation image-definable equivalence relations equation image such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from equation image. It follows that B together with the family of sorts determined by equation image admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean (...)
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