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Profile: Roman Kossak (City University of New York)
  1. Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (2015). Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter.
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  2. John Baldwin, Johanna Ny Franklin, C. Ward Henson, Julia F. Knight, Roman Kossak, Dima Sinapova, W. Hugh Woodin & Philip Scowcroft (2013). John B. Hynes Veterans Memorial Convention Center Boston Marriott Hotel, and Boston Sheraton Hotel Boston, MA January 6–7, 2012. [REVIEW] Bulletin of Symbolic Logic 19 (2).
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  3. Juliette Kennedy & Roman Kossak (eds.) (2012). Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Cambridge University Press.
    Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James H. (...)
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  4. Roman Kossak & James H. Schmerl (2012). On Cofinal Submodels and Elementary Interstices. Notre Dame Journal of Formal Logic 53 (3):267-287.
    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 (...)
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  5. Samuel Coskey & Roman Kossak (2010). The Complexity of Classification Problems for Models of Arithmetic. Bulletin of Symbolic Logic 16 (3):345-358.
    We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.
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  6. Roman Kossak (2006). The Notre Dame Lectures, Edited by Cholak Peter, Lecture Notes in Logic, Vol. 18. Association for Symbolic Logic, AK Peters, Ltd., Wellesley, Massachusetts, 2005, Vii+ 185 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (4):605-607.
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  7. Roman Kossak (2004). A Note on a Theorem of Kanovei. Archive for Mathematical Logic 43 (4):565-569.
    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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  8. Roman Kossak (2004). Undefinability of Truth and Nonstandard Models. Annals of Pure and Applied Logic 126 (1-3):115-123.
    We discuss Robinson's model theoretic proof of Tarski's theorem on undefinability of truth. We present two other “diagonal-free” proofs of Tarski's theorem, and we compare undefinability of truth to other forms of undefinability in nonstandard models of arithmetic.
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  9. Roman Kossak & Nicholas Bamber (1996). On Two Questions Concerning the Automorphism Groups of Countable Recursively Saturated Models of PA. Archive for Mathematical Logic 36 (1):73-79.
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  10. Roman Kossak (1995). Four Problems Concerning Recursively Saturated Models of Arithmetic. Notre Dame Journal of Formal Logic 36 (4):519-530.
    The paper presents four open problems concerning recursively saturated models of Peano Arithmetic. One problems concerns a possible converse to Tarski's undefinability of truth theorem. The other concern elementary cuts in countable recursively saturated models, extending automorphisms of countable recursively saturated models, and Jonsson models of PA. Some partial answers are given.
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  11. Roman Kossak & James H. Schmerl (1995). Arithmetically Saturated Models of Arithmetic. Notre Dame Journal of Formal Logic 36 (4):531-546.
    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 substructures.
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  12. Roman Kossak, Henryk Kotlarski & James H. Schmerl (1993). On Maximal Subgroups of the Automorphism Group of a Countable Recursively Saturated Model of PA. Annals of Pure and Applied Logic 65 (2):125-148.
    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 (...)
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  13. Roman Kossak & Henryk Kotlarski (1992). Game Approximations of Satisfaction Classes Models. Mathematical Logic Quarterly 38 (1):21-26.
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  14. Roman Kossak & Jeffrey B. Paris (1992). Subsets of Models of Arithmetic. Archive for Mathematical Logic 32 (1):65-73.
    We define certain properties of subsets of models of arithmetic related to their codability in end extensions and elementary end extensions. We characterize these properties using some more familiar notions concerning cuts in models of arithmetic.
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  15. Richard Kaye, Roman Kossak & Henryk Kotlarski (1991). Automorphisms of Recursively Saturated Models of Arithmetic. Annals of Pure and Applied Logic 55 (1):67-99.
    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 classification (...)
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  16. Roman Kossak (1991). The Ω-Like Recursively Saturated Models of Arithmetic. Bulletin of the Section of Logic 20 (3/4):109-109.
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  17. Roman Kossak & James H. Schmerl (1991). Minimal Satisfaction Classes with an Application to Rigid Models of Peano Arithmetic. Notre Dame Journal of Formal Logic 32 (3):392-398.
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  18. Roman Kossak (1989). Models with the Ω-Property. Journal of Symbolic Logic 54 (1):177-189.
    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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  19. Roman Kossak (1989). Models with the $Omega$-Property. Journal of Symbolic Logic 54 (1):177-189.
  20. Roman Kossak, Mark Nadel & James Schmerl (1989). A Note on the Multiplicative Semigroup of Models of Peano Arithmetic. Journal of Symbolic Logic 54 (3):936-940.
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  21. Zofia Adamowicz & Roman Kossak (1988). A Note on BΣn and an Intermediate Induction Schema. Mathematical Logic Quarterly 34 (3):261-264.
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  22. Roman Kossak (1985). A Note on Satisfaction Classes. Notre Dame Journal of Formal Logic 26 (1):1-8.
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  23. Roman Kossak (1985). Recursively Saturated $Omega_1$-Like Models of Arithmetic. Notre Dame Journal of Formal Logic 26 (4):413-422.
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  24. Roman Kossak (1983). A Certain Class of Models of Peano Arithmetic. Journal of Symbolic Logic 48 (2):311-320.
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