10 found
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  1.  8
    On Generic Structures.D. W. Kueker & M. C. Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (2):175-183.
  2.  20
    On the Existence of Atomic Models.M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1189-1194.
    We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T$ is a theory of size $\lambda$ where the principal types are dense, yet $T$ has no atomic model.
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  3.  19
    On Rational Limits of Shelah–Spencer Graphs.Justin Brody & M. C. Laskowski - 2012 - Journal of Symbolic Logic 77 (2):580-592.
    Given a sequence {a n } in (0,1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of Shelah-Spencer graphs G(m, m -αn ). We show that in most cases the model theory is either extremely well-behaved or extremely wild, and characterize when each occurs.
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  4.  4
    Karp Complexity and Classes with the Independence Property.M. C. Laskowski & S. Shelah - 2003 - Annals of Pure and Applied Logic 120 (1-3):263-283.
    A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions K into a set of equivalence classes . We prove that no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled 69–88).
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  5.  21
    The Karp Complexity of Unstable Classes.M. C. Laskowski & S. Shelah - 2001 - Archive for Mathematical Logic 40 (2):69-88.
    A class K of structures is controlled if, for all cardinals λ, the relation of L ∞,λ-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
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  6. Forcing Isomorphism.J. T. Baldwin, M. C. Laskowski & S. Shelah - 1994 - Journal of Symbolic Logic 59 (4):1291-1301.
     
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  7.  31
    Forcing Isomorphism II.M. C. Laskowski & S. Shelah - 1996 - Journal of Symbolic Logic 61 (4):1305-1320.
    If T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion Q such that, in any Q-generic extension of the universe, there are non-isomorphic models M 1 and M 2 of T that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if `c.c.c.' is replaced by other cardinal-preserving adjectives. We also give (...)
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  8.  13
    An Omitting Types Theorem for Saturated Structures.A. D. Greif & M. C. Laskowski - 1993 - Annals of Pure and Applied Logic 62 (2):113-118.
    We define a new topology on the space of strong types of a given theory and use it to state an omitting types theorem for countably saturated models of the theory. As an application we show that if T is a small, stable theory of finite weight such that every elementary extension of the countably saturated model is ω-saturated then every weakly saturated model is ω-saturated.
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  9.  12
    Forcing Isomorphism.J. T. Baldwin, M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1291-1301.
  10.  6
    Tiny Models of Categorical Theories.M. C. Laskowski, A. Pillay & P. Rothmaler - 1992 - Archive for Mathematical Logic 31 (6):385-396.
    We explore the existence and the size of infinite models of categorical theories having cardinality less than the size of the associated Tarski-Lindenbaum algebra. Restricting to totally transcendental, categorical theories we show that “Every tiny model is countable” is independent of ZFC. IfT is trivial there is at most one tiny model, which must be the algebraic closure of the empty set. We give a new proof that there are no tiny models ifT is not totally transcendental and is non-trivial.
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