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John T. Baldwin [68]John Baldwin [41]John W. Baldwin [31]John D. Baldwin [8]
John R. Baldwin [1]
  1. Model Theory and the Philosophy of Mathematical Practice: Formalization Without Foundationalism.John T. Baldwin - 2018 - Cambridge University Press.
    Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of (...)
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  2.  10
    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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  3.  7
    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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  4.  15
    Upward Stability Transfer for Tame Abstract Elementary Classes.John Baldwin, David Kueker & Monica VanDieren - 2006 - Notre Dame Journal of Formal Logic 47 (2):291-298.
    Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation property (...)
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  5.  54
    Axiomatizing Changing Conceptions of the Geometric Continuum I: Euclid-Hilbert†.John T. Baldwin - 2018 - Philosophia Mathematica 26 (3):346-374.
    We give a general account of the goals of axiomatization, introducing a variant on Detlefsen’s notion of ‘complete descriptive axiomatization’. We describe how distinctions between the Greek and modern view of number, magnitude, and proportion impact the interpretation of Hilbert’s axiomatization of geometry. We argue, as did Hilbert, that Euclid’s propositions concerning polygons, area, and similar triangles are derivable from Hilbert’s first-order axioms. We argue that Hilbert’s axioms including continuity show much more than the geometrical propositions of Euclid’s theorems and (...)
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  6.  10
    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.
  7.  2
    Complete Lω1,Ω‐Sentences with Maximal Models in Multiple Cardinalities.John Baldwin & Ioannis Souldatos - 2019 - Mathematical Logic Quarterly 65 (4):444-452.
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  8.  18
    Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descartes-Hilbert-Tarski†.John T. Baldwin - 2019 - Philosophia Mathematica 27 (1):33-60.
    In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi’s for Cartesian geometry and new systems for adding $$\pi$$. In contrast we find Hilbert’s full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.
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  9.  22
    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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  10.  7
    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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  11.  49
    The Stability Spectrum for Classes of Atomic Models.John T. Baldwin & Saharon Shelah - 2012 - Journal of Mathematical Logic 12 (1):1250001-.
    We prove two results on the stability spectrum for Lω1,ω. Here [Formula: see text] denotes an appropriate notion of Stone space of m-types over M. Theorem for unstable case: Suppose that for some positive integer m and for every α μ, K is not i-stable in μ. These results provide a new kind of sufficient condition for the unstable case and shed some light on the spectrum of strictly stable theories in this context. The methods avoid the use of compactness (...)
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  12. 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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  13. Five Discourses on Desire: Sexuality and Gender in Northern France Around 1200.John W. Baldwin - 1991 - Speculum 66 (4):797-819.
    When we think of desire in the Middle Ages we immediately recall the religious exhortation to love God and despise the flesh. My present subject is not the desire for God but the less sublime theme of sexual desire, however the two may have been linked. Sexual desire was a central intellectual concern for medieval thinkers despite their reputed aversion to the subject. It was not, for example, the trifunctional schema of modern celebrity — oratores, bellatores, laboratores — that was (...)
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  14. Almost Strongly Minimal Theories. II.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (4):657-660.
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  15.  11
    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.
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  16.  3
    Almost Galois Ω-Stable Classes.John T. Baldwin, Paul B. Larson & Saharon Shelah - 2015 - Journal of Symbolic Logic 80 (3):763-784.
  17.  3
    How Big Should the Monster Model Be? [REVIEW]John T. Baldwin - 2015 - 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. pp. 31-50.
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  18.  17
    Completeness and Categoricity : Formalization Without Foundationalism.John T. Baldwin - 2014 - Bulletin of Symbolic Logic 20 (1):39-79.
    We propose a criterion to regard a property of a theory as virtuous: the property must have significant mathematical consequences for the theory. We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy extends this virtue to other complete theories. The interaction of (...)
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  19. Meeting of the Association for Symbolic Logic.John Baldwin, D. A. Martin, Robert I. Soare & W. W. Tait - 1976 - Journal of Symbolic Logic 41 (2):551-560.
  20.  12
    A Hanf Number for Saturation and Omission: The Superstable Case.John T. Baldwin & Saharon Shelah - 2014 - Mathematical Logic Quarterly 60 (6):437-443.
  21. Almost Strongly Minimal Theories. I.John T. Baldwin - 1972 - Journal of Symbolic Logic 37 (3):487-493.
  22.  9
    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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  23.  20
    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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  24.  53
    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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  25.  6
    First-Order Theories of Abstract Dependence Relations.John T. Baldwin - 1984 - Annals of Pure and Applied Logic 26 (3):215-243.
  26.  9
    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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  27.  30
    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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  28.  49
    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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  29.  15
    DOP and FCP in Generic Structures.John T. Baldwin & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (2):427-438.
  30.  19
    John W. Rosenthal. A New Proof of a Theorem of Shelah. The Journal of Symbolic Logic, Vol. 37 , Pp. 133–134.John T. Baldwin - 1973 - Journal of Symbolic Logic 38 (4):649.
  31.  18
    Jane Bridge. Beginning Model Theory. The Completeness Theorem and Some Consequences. Oxford Logic Guides. Clarendon Press, Oxford1977, Viii + 143 Pp. [REVIEW]John T. Baldwin - 1979 - Journal of Symbolic Logic 44 (2):283.
  32.  24
    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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  33.  1
    Strongly Minimal Steiner Systems I: Existence.John Baldwin & Gianluca Paolini - forthcoming - Journal of Symbolic Logic:1-15.
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  34.  18
    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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  35.  15
    Saharon Shelah. There Are Just Four Second-Order Quantifiers. Israel Journal of Mathematics, Vol. 15 , Pp. 282–300.John T. Baldwin - 1986 - Journal of Symbolic Logic 51 (1):234.
  36.  3
    Images in Mathematics.John T. Baldwin - forthcoming - Theoria.
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  37.  6
    Trivial Pursuit: Remarks on the Main Gap.John T. Baldwin & Leo Harrington - 1987 - Annals of Pure and Applied Logic 34 (3):209-230.
  38.  12
    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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  39.  11
    Ehud Hrushovski, A New Strongly Minimal Set, Annals of Pure and Applied Logic, Vol. 62 , Pp. 147–166. - Ehud Hrushovski, Strongly Minimal Expansions of Algebraically Closed Fields, Israel Journal of Mathematics, Vol. 79 , Pp. 129–151. [REVIEW]John Baldwin - 1999 - Journal of Symbolic Logic 64 (2):904-905.
  40.  21
    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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  41.  29
    Memoirs of Fellows and Corresponding Fellows of the Mediaeval Academy of America.John W. Baldwin, Ruth J. Dean, Frederic C. Lane, William Roach, Astrik L. Gabriel, Richard P. McKeon, Jaroslav Pelikan, Laurence K. Shook, Robert S. Lopez, Kenneth M. Setton, S. D. Goitein, Gerhart B. Ladner & John F. Leyerle - 1979 - Speculum 54 (3):651-658.
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  42.  29
    Memoirs of Fellows and Corresponding Fellows of the Medieval Academy of America.Paul Meyvaert, B. J. Whiting, Larry D. Benson, Archibald R. Lewis, John W. Baldwin, Morton Bloomfield, Robert Brentano, David Herlihy, William J. Courtenay, Thomas N. Bisson, C. J. Bishko, Ruth J. Dean, Richard H. Rouse, Robert E. Kaske, Otto Springer & Theodore M. Andersson - 1985 - Speculum 60 (3):768-777.
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  43.  5
    Stability Theory and Algebra.John T. Baldwin - 1979 - Journal of Symbolic Logic 44 (4):599-608.
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  44.  22
    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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  45.  27
    Reason and Society in the Middle Ages. Alexander Murray.John W. Baldwin - 1980 - Speculum 55 (3):604-606.
  46.  27
    Memoirs of Fellows and Corresponding Fellows of the Medieval Academy of America.William J. Courtenay, F. Edward Cranz, Franz Rosenthal, Robert L. Benson, Berthe Marti, T. N. Bisson, Larry D. Benson, George Kane, Fred C. Robinson, Leonard Boyle, Brian Tierney, Stephan Kuttner, Robert Hanning, John Pope, Samuel Thorne, John W. Baldwin, Theodore M. Andersson, Archibald R. Lewis, Jaroslav Pelikan, David Herlihy, John Leyerle, John H. Fisher, Ruth J. Dean, William J. Roach, Siegfried Wenzel, Archibald L. Lewis, Bryce Lyon, G. P. Cuttino, John F. Benton, Marshall Clagett, Richard H. Rouse & Edward Grant - 1988 - Speculum 63 (3):755-771.
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  47.  19
    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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  48.  17
    Some EC∑ Classes of Rings.John T. Baldwin - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (31-36):489-492.
  49.  24
    Religious Thought and Economic Society: Four Chapters of an Unfinished Work. Jacob Viner.John Baldwin - 1980 - Speculum 55 (4):853-855.
  50.  34
    Let's Go All the Way – and Include Operant and Observational Learning.John D. Baldwin - 2000 - Behavioral and Brain Sciences 23 (2):249-250.
    If biologists are going to incorporate learning into theories of animal behavior, why not go all the way and incorporate the enormous literatures on Pavlovian conditioning, plus those on operant and observational learning?
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