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  1. On Model-Completeness.Per Lindström - 1964 - Theoria 30 (3):183-196.
  • Model Companions of $T_{\rm Aut}$ for Stable T.John T. Baldwin & Saharon Shelah - 2001 - Notre Dame Journal of Formal Logic 42 (3):129-142.
    We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property . For any theory T, form a new theory $T_{\rm Aut}$ by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if $T_{\rm Aut}$ has a model companion. (...)
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  • Model Companions of for Stable T.John T. Baldwin & Saharon Shelah - 2001 - Notre Dame Journal of Formal Logic 42 (3):129-142.
    We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if has a model companion. The proof involves some (...)
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  • Expansions of Geometries.John T. Baldwin - 2003 - Journal of Symbolic Logic 68 (3):803-827.
    For $n < \omega$ , expand the structure (n, S, I, F) (with S the successor relation, I, F as the initial and final element) by forming graphs with edge probability n-α for irrational α, with $0 < \alpha < 1$ . The sentences in the expanded language, which have limit probability 1, form a complete and stable theory.
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  • Ultraproducts Which Are Not Saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.
    In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...)
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  • Transfering Saturation, the Finite Cover Property, and Stability.John T. Baldwin, Rami Grossberg & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (2):678-684.
    $\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ if and only if there is an expansion T 1 of T with ∣ T 1 ∣ = ∣ T ∣ such that if M is a μ-saturated model of T 1 and ∣ M ∣ ≥ κ then the reduct M ∣ L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (ℵ 0 , λ)- transferable or (κ (T), λ)-transferable for all λ. (...)
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  • Probabilities on Finite Models.Ronald Fagin - 1976 - Journal of Symbolic Logic 41 (1):50-58.
  • Almost Everywhere Equivalence of Logics in Finite Model Theory.Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto - 1996 - Bulletin of Symbolic Logic 2 (4):422-443.
    We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L ′ are two logics and μ is an asymptotic measure on finite structures, then $\scr{L}\equiv _{\text{a.e.}}\scr{L}^{\prime}(\mu)$ means that there is a class C of finite structures with μ (C)=1 (...)
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  • DOP and FCP in Generic Structures.John T. Baldwin & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (2):427-438.
  • Constructing Ω-Stable Structures: Model Completeness.John T. Baldwin & Kitty Holland - 2004 - Annals of Pure and Applied Logic 125 (1-3):159-172.
    The projective plane of Baldwin 695) is model complete in a language with additional constant symbols. The infinite rank bicolored field of Poizat 1339) is not model complete. The finite rank bicolored fields of Baldwin and Holland 371; Notre Dame J. Formal Logic , to appear) are model complete. More generally, the finite rank expansions of a strongly minimal set obtained by adding a ‘random’ unary predicate are almost strongly minimal and model complete provided the strongly minimal set is ‘well-behaved’ (...)
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  • Paires de Structures Stables.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (2):239-249.