21 found
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Charles Steinhorn [20]Charles I. Steinhorn [2]
  1.  11
    Expansions of o-Minimal Structures by Dense Independent Sets.Alfred Dolich, Chris Miller & Charles Steinhorn - 2016 - Annals of Pure and Applied Logic 167 (8):684-706.
  2.  23
    Pseudofinite Structures and Simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
    We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are (...)
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  3.  8
    On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
  4.  20
    Definable Types in o-Minimal Theories.David Marker & Charles I. Steinhorn - 1994 - Journal of Symbolic Logic 59 (1):185-198.
  5.  5
    Definable Types in $Mathscr{O}$-Minimal Theories.David Marker & Charles I. Steinhorn - 1994 - Journal of Symbolic Logic 59 (1):185-198.
  6.  12
    Extensions of Ordered Theories by Generic Predicates.Alfred Dolich, Chris Miller & Charles Steinhorn - 2013 - Journal of Symbolic Logic 78 (2):369-387.
  7.  2
    Discrete o-Minimal Structures.Anand Pillay & Charles Steinhorn - 1987 - Annals of Pure and Applied Logic 34 (3):275-289.
  8.  5
    Uncountable Real Closed Fields with Pa Integer Parts.David Marker, James H. Schmerl & Charles Steinhorn - 2015 - Journal of Symbolic Logic 80 (2):490-502.
  9.  14
    On Linearly Ordered Structures of Finite Rank.Alf Onshuus & Charles Steinhorn - 2009 - Journal of Mathematical Logic 9 (2):201-239.
    O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all (...)
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  10.  18
    On o-Minimal Expansions of Archimedean Ordered Groups.Michael C. Laskowski & Charles Steinhorn - 1995 - Journal of Symbolic Logic 60 (3):817-831.
    We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion of R. (...)
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  11.  33
    Extending Partial Orders on o‐Minimal Structures to Definable Total Orders.Dugald Macpherson & Charles Steinhorn - 1997 - Mathematical Logic Quarterly 43 (4):456-464.
    It is shown that if is an o-minimal structure such that is a dense total order and ≾ is a parameter-definable partial order on M, then ≾ has an extension to a definable total order.
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  12.  9
    A Note on Nonmultidimensional Superstable Theories.Anand Pillay & Charles Steinhorn - 1985 - Journal of Symbolic Logic 50 (4):1020-1024.
  13.  16
    Wilkie A. J., Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function, Journal of the American Mathematical Society, Vol. 9 , Pp. 1051–1094. [REVIEW]Charles Steinhorn - 1999 - Journal of Symbolic Logic 64 (2):910-913.
  14. The Nonαxiomαtizαbility of 1.(0^) by Finitely Many Schemata.Saharon Shelah & Charles Steinhorn - 1990 - Notre Dame Journal of Formal Logic 31 (1):1-13.
  15.  7
    The Nonaxiomatizability of $L(Q^2{\Aleph1})$ by Finitely Many Schemata.Saharon Shelah & Charles Steinhorn - 1989 - Notre Dame Journal of Formal Logic 31 (1):1-13.
  16.  2
    On the Nonaxiomatizability of Some Logics by Finitely Many Schemas.Saharon Shelah & Charles Steinhorn - 1986 - Notre Dame Journal of Formal Logic 27 (1):1-11.
  17.  22
    On Dedekind Complete o-Minimal Structures.Anand Pillay & Charles Steinhorn - 1987 - Journal of Symbolic Logic 52 (1):156-164.
    For a countable complete o-minimal theory T, we introduce the notion of a sequentially complete model of T. We show that a model M of T is sequentially complete if and only if $\mathscr{M} \prec \mathscr{N}$ for some Dedekind complete model N. We also prove that if T has a Dedekind complete model of power greater than 2 ℵ 0 , then T has Dedekind complete models of arbitrarily large powers. Lastly, we show that a dyadic theory--namely, a theory relative (...)
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  18.  15
    The Boolean Spectrum of an $o$-Minimal Theory.Charles Steinhorn & Carlo Toffalori - 1989 - Notre Dame Journal of Formal Logic 30 (2):197-206.
  19.  10
    1995–1996 Annual Meeting of the Association for Symbolic Logic.Tomek Bartoszynski, Harvey Friedman, Geoffrey Hellman, Bakhadyr Khoussainov, Phokion G. Kolaitis, Richard Shore, Charles Steinhorn, Mirna Dzamonja, Itay Neeman & Slawomir Solecki - 1996 - Bulletin of Symbolic Logic 2 (4):448-472.
  20.  8
    Definably Extending Partial Orders in Totally Ordered Structures.Janak Ramakrishnan & Charles Steinhorn - 2014 - Mathematical Logic Quarterly 60 (3):205-210.
  21.  9
    Review: A. J. Wilkie, Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function. [REVIEW]Charles Steinhorn - 1999 - Journal of Symbolic Logic 64 (2):910-913.