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75Open days in set theory and arithmetic, Jachranka, Poland, 1986Journal of Symbolic Logic 52 (3): 888-894. 1987.
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80Minimal satisfaction classes with an application to rigid models of Peano arithmeticNotre Dame Journal of Formal Logic 32 (3): 392-398. 1991.
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57The ω-like recursively saturated models of arithmeticBulletin of the Section of Logic 20 (3/4): 109-109. 1991.
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77Game approximations of satisfaction classes modelsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1): 21-26. 1992.
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139Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics (edited book)De Gruyter. 2015.In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.
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52Preface – Unity and Diversity of LogicIn Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, De Gruyter. 2015.
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68On maximal subgroups of the automorphism group of a countable recursively saturated model of PAAnnals of Pure and Applied Logic 65 (2): 125-148. 1993.We show that the stabilizer of an element a of a countable recursively saturated model of arithmetic M is a maximal subgroup of Aut iff the type of a is selective. This is a point of departure for a more detailed study of the relationship between pointwise and setwise stabilizers of certain subsets of M and the types of elements in those subsets. We also show that a complete type of PA is 2-indiscernible iff it is minimal in the sense of Gaifman
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103A note on the multiplicative semigroup of models of peano arithmeticJournal of Symbolic Logic 54 (3): 936-940. 1989.
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65Recursively saturated $\omega_1$-like models of arithmeticNotre Dame Journal of Formal Logic 26 (4): 413-422. 1985.
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165Models with the ω-propertyJournal of Symbolic Logic 54 (1): 177-189. 1989.A model M of PA has the omega-property if it has a subset of order type omega that is coded in an elementary end extension of M. All countable recursively saturated models have the omega-property, but there are also models with the omega-property that are not recursively saturated. The papers is devoted to the study of structural properties of such models.
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120Automorphism group actions on treesMathematical Logic Quarterly 50 (1): 71. 2004.We study the situation when the automorphism group of a recursively saturated structure acts on an ℝ-tree. The cases of and models of Peano Arithmetic are central in the paper
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84Arithmetically Saturated Models of ArithmeticNotre Dame Journal of Formal Logic 36 (4): 531-546. 1995.The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. We consider questions concerning the automorphism group of a countable recursively saturated model of PA. We prove new results concerning fixed point sets, open subgroups, and the cofinality of the automorphism group. We also prove that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of its elementary substructur…Read more
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72On two questions concerning the automorphism groups of countable recursively saturated models of PAArchive for Mathematical Logic 36 (1): 73-79. 1996.
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52A note on a theorem of KanoveiArchive for Mathematical Logic 43 (4): 565-569. 2004.We give a short proof of a theorem of Kanovei on separating induction and collection schemes for Σ n formulas using families of subsets of countable models of arithmetic coded in elementary end extensions
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96A Note on BΣn and an Intermediate Induction SchemaZeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3): 261-264. 1988.
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48A Radio Interview with Jouko VäänänenIn Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, De Gruyter. pp. 417-422. 2015.
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34The Structure of Models of Peano ArithmeticClarendon Press. 2006.Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.
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78On Cofinal Submodels and Elementary IntersticesNotre Dame Journal of Formal Logic 53 (3): 267-287. 2012.We prove a number of results concerning the variety of first-order theories and isomorphism types of pairs of the form $(N,M)$ , where $N$ is a countable recursively saturated model of Peano Arithmetic and $M$ is its cofinal submodel. We identify two new isomorphism invariants for such pairs. In the strongest result we obtain continuum many theories of such pairs with the fixed greatest common initial segment of $N$ and $M$ and fixed lattice of interstructures $K$ , such that $M\prec K\prec N$
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79Automorphisms of recursively saturated models of arithmeticAnnals of Pure and Applied Logic 55 (1): 67-99. 1991.We give an examination of the automorphism group Aut of a countable recursively saturated model M of PA. The main result is a characterisation of strong elementary initial segments of M as the initial segments consisting of fixed points of automorphisms of M. As a corollary we prove that, for any consistent completion T of PA, there are recursively saturated countable models M1, M2 of T, such that Aut[ncong]Aut, as topological groups with a natural topology. Other results include a classificatio…Read more
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CUNY Graduate CenterRegular Faculty
New York City, New York, United States of America
Areas of Interest
| Logic and Philosophy of Logic |
| European Philosophy |