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  1.  34
    On the Boolean Algebras of Definable Sets in Weakly o‐Minimal Theories.Stefano Leonesi & Carlo Toffalori - 2004 - Mathematical Logic Quarterly 50 (3):241-248.
    We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within (...)
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  2.  23
    Filling Certain Cuts in Discrete Weakly o-Minimal Structures.Stefano Leonesi & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (2):145.
    Discrete weakly o-minimal structures, although not so stimulating as their dense counterparts, do exhibit a certain wealth of examples and pathologies. For instance they lack prime models and monotonicity for definable functions, and are not preserved by elementary equivalence. First we exhibit these features. Then we consider a countable theory of weakly o-minimal structures with infinite definable discrete subsets and we study the Boolean algebra of definable sets of its countable models.
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  3.  4
    Weakly Minimal Modules Over Integral Group Rings and Over Related Classes of Rings.Stefano Leonesi, Sonia L'Innocente & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (6):613-625.
    A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prüfer domains and integral group rings.
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