16 found
Order:
  1.  16
    Vapnik–Chervonenkis Density in Some Theories Without the Independence Property, II.Matthias Aschenbrenner, Alf Dolich, Deirdre Haskell, Dugald Macpherson & Sergei Starchenko - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):311-363.
    We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  2.  45
    A Version of o-Minimality for the P-Adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
  3.  11
    Cell Decompositions of C-Minimal Structures.Deirdre Haskell & Dugald Macpherson - 1994 - Annals of Pure and Applied Logic 66 (2):113-162.
    C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  4.  6
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  5.  51
    Grothendieck Rings of ℤ-Valued Fields.Raf Cluckers & Deirdre Haskell - 2001 - Bulletin of Symbolic Logic 7 (2):262-269.
    We prove the triviality of the Grothendieck ring of a Z-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K 2 to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  68
    Model Theory of Analytic Functions: Some Historical Comments.Deirdre Haskell - 2012 - Bulletin of Symbolic Logic 18 (3):368-381.
    Model theorists have been studying analytic functions since the late 1970s. Highlights include the seminal work of Denef and van den Dries on the theory of the p-adics with restricted analytic functions, Wilkie's proof of o-minimality of the theory of the reals with the exponential function, and the formulation of Zilber's conjecture for the complex exponential. My goal in this talk is to survey these main developments and to reflect on today's open problems, in particular for theories of valued fields.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark  
  7.  10
    Denef J. And van den Dries L.. P-Adic and Real Subanalytic Sets. Annals of Mathematics, Ser. 2 Vol. 128 , Pp. 79–138.Deirdre Haskell - 1997 - Journal of Symbolic Logic 62 (4):1481-1483.
  8.  23
    Ganzstellensätze in Theories of Valued Fields.Deirdre Haskell & Yoav Yaffe - 2008 - Journal of Mathematical Logic 8 (1):1-22.
    The purpose of this paper is to study an analogue of Hilbert's seventeenth problem for functions over a valued field which are integral definite on some definable set; that is, that map the given set into the valuation ring. We use model theory to exhibit a uniform method, on various theories of valued fields, for deriving an algebraic characterization of such functions. As part of this method we refine the concept of a function being integral at a point, and make (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  9.  13
    A Note on Valuation Definable Expansions of Fields.Deirdre Haskell & Dugald Macpherson - 1998 - Journal of Symbolic Logic 63 (2):739-743.
  10.  8
    Review: J. Denef, L. Van den Dries, $ P $-Adic and Real Subanalytic Sets. [REVIEW]Deirdre Haskell - 1997 - Journal of Symbolic Logic 62 (4):1481-1483.
  11.  9
    A Transfer Theorem in Constructive P-Adic Algebra.Deirdre Haskell - 1992 - Annals of Pure and Applied Logic 58 (1):29-55.
    The main result of this paper is a transfer theorem which describes the relationship between constructive validity and classical validity for a class of first-order sentences over the p-adics. The proof of one direction of the theorem uses a principle of intuitionism; the proof of the other direction is classically valid. Constructive verifications of known properties of the p-adics are indicated. In particular, the existence of cylindric algebraic decompositions for the p-adics is used.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  12.  8
    University of California at Berkeley Berkeley, CA, USA March 24–27, 2011.G. Aldo Antonelli, Laurent Bienvenu, Lou van den Dries, Deirdre Haskell, Justin Moore, Christian Rosendal Uic, Neil Thapen & Simon Thomas - 2012 - Bulletin of Symbolic Logic 18 (2).
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  13.  6
    Unexpected Imaginaries in Valued Fields with Analytic Structure.Deirdre Haskell, Ehud Hrushovski & Dugald Macpherson - 2013 - Journal of Symbolic Logic 78 (2):523-542.
    We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  14.  6
    Grothendieck Rings of $Mathbb{Z}$-Valued Fields.Raf Cluckers & Deirdre Haskell - 2001 - Bulletin of Symbolic Logic 7 (2):262-269.
    We prove the triviality of the Grothendieck ring of a $\mathbb{Z}$-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K$^2$ to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15. Stanford University, Stanford, CA March 19–22, 2005.Steve Awodey, Raf Cluckers, Ilijas Farah, Solomon Feferman, Deirdre Haskell, Andrey Morozov, Vladimir Pestov, Andre Scedrov, Andreas Weiermann & Jindrich Zapletal - 2006 - Bulletin of Symbolic Logic 12 (1).
     
    Export citation  
     
    Bookmark  
  16.  3
    2005 Annual Meeting of the Association for Symbolic Logic.Ilijas Farah, Deirdre Haskell, Andrey Morozov, Vladimir Pestov & Jindrich Zapletal - 2006 - Bulletin of Symbolic Logic 12 (1):143.