58 found
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  1.  4
    Disjoint Amalgamation in Locally Finite Aec.John T. Baldwin, Martin Koerwien & Michael C. Laskowski - 2017 - Journal of Symbolic Logic 82 (1):98-119.
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  2.  3
    Categoricity.John T. Baldwin - 2009 - American Mathematical Society.
    CHAPTER 1 Combinatorial Geometries and Infinitary Logics In this chapter we introduce two of the key concepts that are used throughout the text. ...
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  3. Almost Strongly Minimal Theories. II.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (4):657-660.
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  4. Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
    Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. In (...)
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  5. Classification of Δ-Invariant Amalgamation Classes.Roman D. Aref'ev, John T. Baldwin & Marco Mazzucco - 1999 - Journal of Symbolic Logic 64 (4):1743-1750.
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  6. Almost Galois Ω-Stable Classes.John T. Baldwin, Paul B. Larson & Saharon Shelah - 2015 - Journal of Symbolic Logic 80 (3):763-784.
  7.  17
    Formalization, Primitive Concepts, and Purity.John T. Baldwin - 2012 - Review of Symbolic Logic 1 (1):1-42.
    We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedyformalism freenessspatial contents through algebra, of the embedding theorem.
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  8.  11
    Examples of Non-Locality.John T. Baldwin & Saharon Shelah - 2008 - Journal of Symbolic Logic 73 (3):765-782.
    We use κ-free but not Whitehead Abelian groups to constructElementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-types. We introduce the notion that an AEC admits intersections. We conclude that for AEC which admit intersections, the amalgamation property can have no positive effect on locality: there is a transformation of AEC's which preserves non-locality but takes any AEC which admits intersections to one with amalgamation. More specifically we have: Theorem 5.3. There is (...)
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  9. Almost Strongly Minimal Theories. I.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (3):487-493.
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  10. A Hanf Number for Saturation and Omission: The Superstable Case.John T. Baldwin & Saharon Shelah - 2014 - Mathematical Logic Quarterly 60 (6):437-443.
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  11.  4
    First-Order Theories of Abstract Dependence Relations.John T. Baldwin - 1984 - Annals of Pure and Applied Logic 26 (3):215-243.
  12.  4
    The Amalgamation Spectrum.John T. Baldwin, Alexei Kolesnikov & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (3):914-928.
    We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of cardinality $\mathfrak{N}_{k (...)
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  13.  22
    The Stability Spectrum for Classes of Atomic Models.John T. Baldwin & Saharon Shelah - 2012 - Journal of Mathematical Logic 12 (01):1250001-.
  14.  3
    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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  15.  2
    As an Abstract Elementary Class.John T. Baldwin, Paul C. Eklof & Jan Trlifaj - 2007 - Annals of Pure and Applied Logic 149 (1):25-39.
    In this paper we study abstract elementary classes of modules. We give several characterizations of when the class of modules A with is abstract elementary class with respect to the notion that M1 is a strong submodel M2 if the quotient remains in the given class.
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  16.  6
    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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  17.  2
    DOP and FCP in Generic Structures.John T. Baldwin & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (2):427-438.
  18.  28
    Constructing Ω-Stable Structures: Rank 2 Fields.John T. Baldwin & Kitty Holland - 2000 - Journal of Symbolic Logic 65 (1):371-391.
    We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an expansion (...)
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  19.  3
    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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  20.  16
    Some EC∑ Classes of Rings.John T. Baldwin - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (31-36):489-492.
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  21.  10
    K‐Generic Projective Planes Have Morley Rank Two or Infinity.John T. Baldwin & Masanori Itai - 1994 - Mathematical Logic Quarterly 40 (2):143-152.
    We show that K-generic projective planes have Morley rank either two or infinity. We also show give a direct argument that such planes are not Desarguesian.
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  22.  4
    The Metamathematics of Random Graphs.John T. Baldwin - 2006 - Annals of Pure and Applied Logic 143 (1):20-28.
    We explain and summarize the use of logic to provide a uniform perspective for studying limit laws on finite probability spaces. This work connects developments in stability theory, finite model theory, abstract model theory, and probability. We conclude by linking this context with work on the Urysohn space.
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  23.  11
    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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  24.  1
    Trivial Pursuit: Remarks on the Main Gap.John T. Baldwin & Leo Harrington - 1987 - Annals of Pure and Applied Logic 34 (3):209-230.
  25.  4
    Algebraically Prime Models.John T. Baldwin & David W. Keuker - 1981 - Annals of Mathematical Logic 20 (3):289-330.
  26.  25
    Some Contributions to Definability Theory for Languages with Generalized Quantifiers.John T. Baldwin & Douglas E. Miller - 1982 - Journal of Symbolic Logic 47 (3):572-586.
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  27.  3
    Stability Theory and Algebra.John T. Baldwin - 1979 - Journal of Symbolic Logic 44 (4):599-608.
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  28.  1
    Some EC∑ Classes of Rings.John T. Baldwin - 1978 - Mathematical Logic Quarterly 24 (31‐36):489-492.
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  29.  8
    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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  30.  5
    Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (2):222-223.
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  31.  15
    Local Homogeneity.Bektur Baizhanov & John T. Baldwin - 2004 - Journal of Symbolic Logic 69 (4):1243 - 1260.
    We study the expansion of stable structures by adding predicates for arbitrary subsets. Generalizing work of Poizat-Bouscaren on the one hand and Baldwin-Benedikt-Casanovas-Ziegler on the other we provide a sufficient condition (Theorem 4.7) for such an expansion to be stable. This generalization weakens the original definitions in two ways: dealing with arbitrary subsets rather than just submodels and removing the 'small' or 'belles paires' hypothesis. We use this generalization to characterize in terms of pairs, the 'triviality' of the geometry on (...)
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  32.  14
    Meeting of the Association for Symbolic Logic: Biloxi, 1979.Daniel Halpern, William Tait & John T. Baldwin - 1981 - Journal of Symbolic Logic 46 (1):191-198.
  33.  19
    Notes on Quasiminimality and Excellence.John T. Baldwin - 2004 - Bulletin of Symbolic Logic 10 (3):334-366.
    This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) (...)
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  34.  6
    Categoricity and Generalized Model Completeness.G. Ahlbrandt & John T. Baldwin - 1988 - Archive for Mathematical Logic 27 (1):1-4.
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  35.  11
    A Model Theoretic Approach to Malcev Conditions.John T. Baldwin & Joel Berman - 1977 - Journal of Symbolic Logic 42 (2):277-288.
  36.  12
    The Spectrum of Resplendency.John T. Baldwin - 1990 - Journal of Symbolic Logic 55 (2):626-636.
    Let T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2 λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least $\min(2^\lambda,\beth_2)$ resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, (...)
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  37.  2
    Completeness and Categoricity : Formalization Without Foundationalism.John T. Baldwin - 2014 - Bulletin of Symbolic Logic 20 (1):39-79.
  38.  11
    The Vaught Conjecture: Do Uncountable Models Count?John T. Baldwin - 2007 - Notre Dame Journal of Formal Logic 48 (1):79-92.
    We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{ω₁,ω}$-types. The following result is new. Theorem: If a first-order theory is a counterexample to the Vaught Conjecture then it has 2\sp ℵ₁ models of cardinality ℵ₁.
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  39.  2
    Iterated Elementary Embeddings and the Model Theory of Infinitary Logic.John T. Baldwin & Paul B. Larson - 2016 - Annals of Pure and Applied Logic 167 (3):309-334.
  40.  9
    Constructing Ω-Stable Structures: Rank K-Fields.John T. Baldwin & Kitty Holland - 2003 - Notre Dame Journal of Formal Logic 44 (3):139-147.
    Theorem: For every k, there is an expansion of the theory of algebraically closed fields (of any fixed characteristic) which is almost strongly minimal with Morley rank k.
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  41.  2
    Preface.John T. Baldwin - 1993 - Annals of Pure and Applied Logic 62 (2):81.
  42.  1
    Reviews. Selected Papers of Abraham Robinson. Volume 1. Model Theory and Algebra. Edited and with an Introduction by H. J. Keisler. Yale University Press, New Haven and London 1979, Xxxvii + 694 Pp. George B. Selioman. Biography of Abraham Robinson, Pp. Xiii–Xxxii. H. J. Keisler. Introduction, Pp. Xxxiii–Xxxvii. Abraham Robinson. On the Application of Symbolic Logic to Algebra, Pp. 3–11. A Reprint of XVIII 182. Abraham Robinson. Recent Developments in Model Theory, Pp. 12–31. A Reprint of XL 269. Abraham Robinson. On the Construction of Models, Pp. 32–42. A Reprint of XL 506. Abraham Robinson, Metamathematical Problems, Pp. 43–59. , Pp. 500–516.) Abraham Robinson. Model Theory as a Framework for Algebra, Pp. 60–83. Abraham Robinson. A Result on Consistency and its Application to the Theory of Definition, Pp. 87–98. A Reprint of XXV 174. Abraham Robinson. Ordered Structures and Related Concepts, Pp. 99–104. A Reprint of XXV 170. [REVIEW]John T. Baldwin - 1982 - Journal of Symbolic Logic 47 (1):197-203.
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  43.  1
    Shelah S.. Stable Theories. Israel Journal of Mathematics, Vol. 7 , Pp. 187–202.Shelah Saharon. Stability, the F.C.P., and Superstability; Model Theoretic Properties of Formulas in First Order Theory. Annals of Mathematical Logic, Vol. 3 No. 3 , Pp. 271–362. [REVIEW]John T. Baldwin - 1973 - Journal of Symbolic Logic 38 (4):648-649.
  44.  6
    Subsets of Superstable Structures Are Weakly Benign.Bektur Baizhanov, John T. Baldwin & Saharon Shelah - 2005 - Journal of Symbolic Logic 70 (1):142 - 150.
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  45. E-mail: marat@ niimm. kazan. su.John T. Baldwin & Masanori Itai - 1995 - Bulletin of Symbolic Logic 1 (1).
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  46. Review: H. J. Keisler, A. Robinson, Selected Papers of Abraham Robinson.: Model Theory and Algebra. [REVIEW]John T. Baldwin - 1982 - Journal of Symbolic Logic 47 (1):197-203.
     
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  47.  2
    Preface.John T. Baldwin & Annalisa Marcja - 1989 - Annals of Pure and Applied Logic 45 (2):103.
  48.  2
    Diverse Classes.John T. Baldwin - 1989 - Journal of Symbolic Logic 54 (3):875-893.
    Let $\mathbf{I}(\mu,K)$ denote the number of nonisomorphic models of power $\mu$ and $\mathbf{IE}(\mu,K)$ the number of nonmutually embeddable models. We define in this paper the notion of a diverse class and use it to prove a number of results. The major result is Theorem B: For any diverse class $K$ and $\mu$ greater than the cardinality of the language of $K$, $\mathbf{IE}(\mu,K) \geq \min(2^\mu,\beth_2).$ From it we deduce both an old result of Shelah, Theorem C: If $T$ is countable and (...)
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  49.  2
    Review: Saharon Shelah, There Are Just Four Second-Order Quantifiers. [REVIEW]John T. Baldwin - 1986 - Journal of Symbolic Logic 51 (1):234-234.
  50.  1
    Review: Jane Bridge, Begining Model Theory. The Completeness Theorem and Some Consequences. [REVIEW]John T. Baldwin - 1979 - Journal of Symbolic Logic 44 (2):283-283.
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