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  1. John T. Baldwin (2015). How Big Should the Monster Model Be? [REVIEW] In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter 31-50.
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  2. John T. Baldwin & Saharon Shelah (2014). A Hanf Number for Saturation and Omission: The Superstable Case. Mathematical Logic Quarterly 60 (6):437-443.
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  3. John T. Baldwin (2012). Formalization, Primitive Concepts, and Purity. 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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  4. John T. Baldwin & Saharon Shelah (2012). The Stability Spectrum for Classes of Atomic Models. Journal of Mathematical Logic 12 (01):1250001-.
  5. John T. Baldwin (2009). Categoricity. 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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  6. John T. Baldwin, Alexei Kolesnikov & Saharon Shelah (2009). The Amalgamation Spectrum. 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 $\mathfrak{N}_{k (...)
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  7. John T. Baldwin & Saharon Shelah (2008). Examples of Non-Locality. Journal of Symbolic Logic 73 (3):765-782.
    We use κ-free but not Whitehead Abelian groups to constructElementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-types. We introduce the notion that an AEC admits intersections. We conclude that for AEC which admit intersections, the amalgamation property can have no positive effect on locality: there is a transformation of AEC's which preserves non-locality but takes any AEC which admits intersections to one with amalgamation. More specifically we have: Theorem 5.3. There is (...)
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  8. John T. Baldwin (2007). The Vaught Conjecture: Do Uncountable Models Count? Notre Dame Journal of Formal Logic 48 (1):79-92.
    We give a model theoretic proof, replacing admissible set theory by the Lopez-Escobar theorem, of Makkai's theorem: Every counterexample to Vaught's Conjecture has an uncountable model which realizes only countably many ℒ$_{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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  9. John T. Baldwin, Paul C. Eklof & Jan Trlifaj (2007). As an Abstract Elementary Class. 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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  10. John T. Baldwin (2006). The Metamathematics of Random Graphs. 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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  11. John T. Baldwin & Olivier Lessmann (2006). Uncountable Categoricity of Local Abstract Elementary Classes with Amalgamation. 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.
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  12. Bektur Baizhanov, John T. Baldwin & Saharon Shelah (2005). Subsets of Superstable Structures Are Weakly Benign. Journal of Symbolic Logic 70 (1):142 - 150.
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  13. Bektur Baizhanov & John T. Baldwin (2004). Local Homogeneity. 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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  14. John T. Baldwin (2004). Notes on Quasiminimality and Excellence. 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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  15. John T. Baldwin (2004). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. Bulletin of Symbolic Logic 10 (2):222-223.
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  16. John T. Baldwin & Kitty Holland (2004). Constructing Ω-Stable Structures: Model Completeness. 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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  17. John T. Baldwin (2003). Expansions of Geometries. 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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  18. John T. Baldwin & Kitty Holland (2003). Constructing Ω-Stable Structures: Rank K-Fields. 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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  19. John T. Baldwin & Saharon Shelah (2001). Model Companions of for Stable T. 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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  20. John T. Baldwin & Saharon Shelah (2001). Model Companions of $T_{\Rm Aut}$ for Stable T. 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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  21. John T. Baldwin & Kitty Holland (2000). Constructing Ω-Stable Structures: Rank 2 Fields. 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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  22. Roman D. Aref'ev, John T. Baldwin & Marco Mazzucco (1999). Classification of Δ-Invariant Amalgamation Classes. Journal of Symbolic Logic 64 (4):1743-1750.
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  23. John T. Baldwin, Rami Grossberg & Saharon Shelah (1999). Transfering Saturation, the Finite Cover Property, and Stability. 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. John T. Baldwin & Saharon Shelah (1998). DOP and FCP in Generic Structures. Journal of Symbolic Logic 63 (2):427-438.
  25. John T. Baldwin & Niandong Shi (1996). Stable Generic Structures. 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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  26. John T. Baldwin & Masanori Itai (1995). E-mail: marat@ niimm. kazan. su. Bulletin of Symbolic Logic 1 (1).
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  27. John T. Baldwin & Masanori Itai (1994). K‐Generic Projective Planes Have Morley Rank Two or Infinity. 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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  28. John T. Baldwin (1993). Preface. Annals of Pure and Applied Logic 62 (2):81.
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  29. John T. Baldwin & Annalisa Marcja (1993). A Selection of Papers Presented at the" Stability in Model Theory III" Conference. Annals of Pure and Applied Logic 62 (2).
     
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  30. John T. Baldwin (1990). The Spectrum of Resplendency. 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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  31. John T. Baldwin (1989). Diverse Classes. 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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  32. John T. Baldwin & Annalisa Marcja (1989). Preface. Annals of Pure and Applied Logic 45 (2):103.
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  33. G. Ahlbrandt & John T. Baldwin (1988). Categoricity and Generalized Model Completeness. Archive for Mathematical Logic 27 (1):1-4.
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  34. John T. Baldwin & Leo Harrington (1987). Trivial Pursuit: Remarks on the Main Gap. Annals of Pure and Applied Logic 34 (3):209-230.
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  35. John T. Baldwin (1986). Review: Saharon Shelah, There Are Just Four Second-Order Quantifiers. [REVIEW] Journal of Symbolic Logic 51 (1):234-234.
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  36. John T. Baldwin (1984). First-Order Theories of Abstract Dependence Relations. Annals of Pure and Applied Logic 26 (3):215-243.
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  37. John T. Baldwin (1982). Review: H. J. Keisler, A. Robinson, Selected Papers of Abraham Robinson.: Model Theory and Algebra. [REVIEW] Journal of Symbolic Logic 47 (1):197-203.
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  38. John T. Baldwin & Douglas E. Miller (1982). Some Contributions to Definability Theory for Languages with Generalized Quantifiers. Journal of Symbolic Logic 47 (3):572-586.
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  39. John T. Baldwin & David W. Keuker (1981). Algebraically Prime Models. Annals of Mathematical Logic 20 (3):289-330.
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  40. Daniel Halpern, William Tait & John T. Baldwin (1981). Meeting of the Association for Symbolic Logic: Biloxi, 1979. Journal of Symbolic Logic 46 (1):191-198.
  41. John T. Baldwin (1979). Review: Jane Bridge, Begining Model Theory. The Completeness Theorem and Some Consequences. [REVIEW] Journal of Symbolic Logic 44 (2):283-283.
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  42. John T. Baldwin (1979). Stability Theory and Algebra. Journal of Symbolic Logic 44 (4):599-608.
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  43. John T. Baldwin (1978). Some EC∑ Classes of Rings. Mathematical Logic Quarterly 24 (31‐36):489-492.
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  44. John T. Baldwin & Joel Berman (1977). A Model Theoretic Approach to Malcev Conditions. Journal of Symbolic Logic 42 (2):277-288.
  45. John T. Baldwin (1973). Review: John W. Rosenthal, A New Proof of a Theorem of Shelah. [REVIEW] Journal of Symbolic Logic 38 (4):649-649.
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  46. John T. Baldwin (1973). Review: S. Shelah, Stable Theories; Saharon Shelah, Stability, the F.C.P., and Superstability; Model Theoretic Properties of Formulas in First Order Theory. [REVIEW] Journal of Symbolic Logic 38 (4):648-649.
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  47. John T. Baldwin (1972). Almost Strongly Minimal Theories. I. Journal of Symbolic Logic 37 (3):487-493.
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  48. John T. Baldwin (1972). Almost Strongly Minimal Theories. II. Journal of Symbolic Logic 37 (4):657-660.
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