9 found
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  1.  23
    Model Completeness of O-Minimal Structures Expanded by Dedekind Cuts.Marcus Tressl - 2005 - Journal of Symbolic Logic 70 (1):29 - 60.
  2.  70
    Axiomatization of Local-Global Principles for Pp-Formulas in Spaces of Orderings.Vincent Astier & Marcus Tressl - 2005 - Archive for Mathematical Logic 44 (1):77-95.
    .We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.
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  3.  18
    Comparison of Exponential-Logarithmic and Logarithmic-Exponential Series.Salma Kuhlmann & Marcus Tressl - 2012 - Mathematical Logic Quarterly 58 (6):434-448.
    We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Thequation image; the elementary theory of the ordered field of real numbers, with the (...)
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  4.  46
    Pseudo Completions and Completions in Stages of o-Minimal Structures.Marcus Tressl - 2006 - Archive for Mathematical Logic 45 (8):983-1009.
    For an o-minimal expansion R of a real closed field and a set $\fancyscript{V}$ of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to $\fancyscript{V}$ . This is an elementary extension S of R generated by all completions of all the residue fields of the $V \in \fancyscript{V}$ , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to an R-isomorphism. For polynomially (...)
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  5.  10
    The Elementary Theory of Dedekind Cuts in Polynomially Bounded Structures.Marcus Tressl - 2005 - Annals of Pure and Applied Logic 135 (1-3):113-134.
    Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M, which yields a description of all subsets of Mn, definable in the expanded structure.
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  6.  11
    Valuation Theoretic Content of the Marker-Steinhorn Theorem.Marcus Tressl - 2004 - Journal of Symbolic Logic 69 (1):91-93.
  7.  17
    Preface.Uri Abraham, Lev Beklemishev, Paola D'Aquino & Marcus Tressl - 2016 - Annals of Pure and Applied Logic 167 (10):865-867.
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  8.  6
    Defining Integer-Valued Functions in Rings of Continuous Definable Functions Over a Topological Field.Luck Darnière & Marcus Tressl - 2020 - Journal of Mathematical Logic 20 (3):2050014.
    Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or (...)
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  9.  31
    Heirs of Box Types in Polynomially Bounded Structures.Marcus Tressl - 2009 - Journal of Symbolic Logic 74 (4):1225 - 1263.
    A box type is an n-type of an o-minimal structure which is uniquely determined by the projections to the coordinate axes. We characterize heirs of box types of a polynomially bounded o-minimal structure M. From this, we deduce various structure theorems for subsets of $M^k $ , definable in the expansion M of M by all convex subsets of the line. We show that M after naming constants, is model complete provided M is model complete.
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