5 found
  1.  11
    O-Minimal Residue Fields of o-Minimal Fields.Jana Maříková - 2011 - Annals of Pure and Applied Logic 162 (6):457-464.
    Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures such that , the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in Maříková [8] it was shown that certain first-order conditions on are sufficient for the o-minimality of . Here we prove that these conditions are also necessary.
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  2.  7
    Residue Field Domination in Real Closed Valued Fields.Clifton Ealy, Deirdre Haskell & Jana Maříková - 2019 - Notre Dame Journal of Formal Logic 60 (3):333-351.
    We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields. We lay some groundwork for extending these results to a power-bounded T-convex theory.
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    Type-Definable and Invariant Groups in O-Minimal Structures.Jana Maříková - 2007 - Journal of Symbolic Logic 72 (1):67 - 80.
    Let M be a big o-minimal structure and G a type-definable group in Mⁿ. We show that G is a type-definable subset of a definable manifold in Mⁿ that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant (...)
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  4.  44
    Geometric Properties of Semilinear and Semibounded Sets.Jana Maříková - 2006 - Mathematical Logic Quarterly 52 (2):190-202.
    We calculate the universal Euler characteristic and universal dimension function on semilinear and semibounded sets and obtain some criteria for definable equivalence of semilinear and semibounded sets in terms of these invariants.
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    Model Completeness of o-Minimal Fields with Convex Valuations.Clifton F. Ealy & Jana Maříková - 2015 - Journal of Symbolic Logic 80 (1):234-250.