14 found
Order:
  1.  18
    Interpreting Groups and Fields in Some Nonelementary Classes.Tapani Hyttinen, Olivier Lessmann & Saharon Shelah - 2005 - Journal of Mathematical Logic 5 (1):1-47.
  2.  12
    Shelah's Stability Spectrum and Homogeneity Spectrum in Finite Diagrams.Rami Grossberg & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (1):1-31.
  3.  8
    A Primer of Simple Theories.Rami Grossberg, José Iovino & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (6):541-580.
    We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  4.  5
    Ranks and Pregeometries in Finite Diagrams.Olivier Lessmann - 2000 - Annals of Pure and Applied Logic 106 (1-3):49-83.
    The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the 0-stable case which share many of the formal properties of forking. This (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  5.  12
    A Rank for the Class of Elementary Submodels of a Superstable Homogeneous Model.Tapani Hyttinen & Olivier Lessmann - 2002 - Journal of Symbolic Logic 67 (4):1469-1482.
    We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence relation (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  6.  6
    Simplicity and Uncountable Categoricity in Excellent Classes.Tapani Hyttinen & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 139 (1):110-137.
    We introduce Lascar strong types in excellent classes and prove that they coincide with the orbits of the group generated by automorphisms fixing a model. We define a new independence relation using Lascar strong types and show that it is well-behaved over models, as well as over finite sets. We then develop simplicity and show that, under simplicity, the independence relation satisfies all the properties of nonforking in a stable first order theory. Further, simplicity for an excellent class, as well (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  7
    Amalgamation Properties and Finite Models in L N -Theories.John Baldwin & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (2):155-167.
    Djordjević [Dj 1] proved that under natural technical assumptions, if a complete L n -theory is stable and has amalgamation over sets, then it has arbitrarily large finite models. We extend his study and prove the existence of arbitrarily large finite models for classes of models of L n -theories (maybe omitting types) under weaker amalgamation properties. In particular our analysis covers the case of vector spaces.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  8.  13
    Upward Categoricity From a Successor Cardinal for Tame Abstract Classes with Amalgamation.Olivier Lessmann - 2005 - Journal of Symbolic Logic 70 (2):639 - 660.
    This paper is devoted to the proof of the following upward categoricity theorem: Let K be a tame abstract elementary class with amalgamation, arbitrarily large models, and countable Löwenheim-Skolem number. If K is categorical in ‮א‬₁ then K is categorical in every uncountable cardinal. More generally, we prove that if K is categorical in a successor cardinal λ⁺ then K is categorical everywhere above λ⁺.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  9.  6
    Canonical Bases in Excellent Classes.Tapani Hyttinen & Olivier Lessmann - 2008 - Journal of Symbolic Logic 73 (1):165-180.
    We show that any (atomic) excellent class K can be expanded with hyperimaginaries to form an (atomic) excellent class Keq which has canonical bases. When K is, in addition, of finite U-rank, then Keq is also simple and has a full canonical bases theorem. This positive situation contrasts starkly with homogeneous model theory for example, where the eq-expansion may fail to be homogeneous. However, this paper shows that expanding an ω-stable, homogeneous class K gives rise to an excellent class, which (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  15
    Local Order Property in Nonelementary Classes.Rami Grossberg & Olivier Lessmann - 2000 - Archive for Mathematical Logic 39 (6):439-457.
    . We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to generalize some of the results that were known in the case of local stability for the (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  11.  10
    Uncountable Categoricity of Local Abstract Elementary Classes with Amalgamation.John T. Baldwin & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 143 (1):29-42.
    We give a complete and elementary proof of the following upward categoricity theorem: let be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable Löwenheim–Skolem number. If is categorical in 1 then is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in first order logic without any use of prime models or heavy stability theoretic machinery.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  12.  6
    2002 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium'02.Lev D. Beklemishev, Stephen Cook, Olivier Lessmann, Simon Thomas, Jeremy Avigad, Arnold Beckmann, Tim Carlson, Robert L. Constable & Kosta Došen - 2003 - Bulletin of Symbolic Logic 9 (1):71.
  13.  3
    A Rank For The Class Of Elementary Submodels Of A Superstable Homogeneous Model.Tapani Hyttinen & Olivier Lessmann - 2002 - Journal of Symbolic Logic 67 (4):1469-1482.
    We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence relation for superstable homogeneous (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  14. Upward Categoricity of Very Tame Abstract Elementary Classes with Amalgamation.John T. Baldwin & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 143 (1-3):29-42.