23 found
Order:
Disambiguations
Rami Grossberg [23]Rami P. Grossberg [1]
  1.  2
    Uniqueness of Limit Models in Classes with Amalgamation.Rami Grossberg, Monica VanDieren & Andrés Villaveces - 2016 - Mathematical Logic Quarterly 62 (4-5):367-382.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   10 citations  
  2.  5
    Canonical Forking in AECs.Will Boney, Rami Grossberg, Alexei Kolesnikov & Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (7):590-613.
  3.  4
    Superstability From Categoricity in Abstract Elementary Classes.Will Boney, Rami Grossberg, Monica M. VanDieren & Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (7):1383-1395.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  4.  3
    Galois-Stability for Tame Abstract Elementary Classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
  5.  6
    Categoricity From One Successor Cardinal in Tame Abstract Elementary Classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (2):181-201.
  6.  8
    Shelah's Categoricity Conjecture From a Successor for Tame Abstract Elementary Classes.Rami Grossberg & Monica VanDieren - 2006 - Journal of Symbolic Logic 71 (2):553 - 568.
    We prove a categoricity transfer theorem for tame abstract elementary classes. Theorem 0.1. Suppose that K is a χ-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let λ ≥ Max{χ.LS(K)⁺}. If K is categorical in λ and λ⁺, then K is categorical in λ⁺⁺. Combining this theorem with some results from [37], we derive a form of Shelah's Categoricity Conjecture for tame abstract elementary classes: Corollary 0.2. Suppose K is a χ-tame (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   15 citations  
  7.  4
    Forking in Short and Tame Abstract Elementary Classes.Will Boney & Rami Grossberg - 2017 - Annals of Pure and Applied Logic 168 (8):1517-1551.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  8.  11
    Shelah's Stability Spectrum and Homogeneity Spectrum in Finite Diagrams.Rami Grossberg & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (1):1-31.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   9 citations  
  9. A Primer of Simple Theories.Rami Grossberg, José Iovino & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (6):541-580.
    We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  10. On the Number of Nonisomorphic Models of an Infinitary Theory Which has the Infinitary Order Property. Part A.Rami Grossberg & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (2):302-322.
    Let κ and λ be infinite cardinals such that κ ≤ λ (we have new information for the case when $\kappa ). Let T be a theory in L κ +, ω of cardinality at most κ, let φ(x̄, ȳ) ∈ L λ +, ω . Now define $\mu^\ast_\varphi (\lambda, T) = \operatorname{Min} \{\mu^\ast:$ If T satisfies $(\forall\mu \kappa)(\exists M_\chi \models T)(\exists \{a_i: i Our main concept in this paper is $\mu^\ast_\varphi (\lambda, \kappa) = \operatorname{Sup}\{\mu^\ast(\lambda, T): T$ is a theory (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  11.  13
    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. (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  12.  21
    Rich Models.Michael H. Albert & Rami P. Grossberg - 1990 - Journal of Symbolic Logic 55 (3):1292-1298.
    We define a rich model to be one which contains a proper elementary substructure isomorphic to itself. Existence, nonstructure, and categoricity theorems for rich models are proved. A theory T which has fewer than $\min(2^\lambda,\beth_2)$ rich models of cardinality $\lambda(\lambda > |T|)$ is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in ℵ 1 and also has a unique countable rich model. We also consider a stronger notion of richness, (...)
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  13.  7
    Indiscernible Sequences in a Model Which Fails to Have the Order Property.Rami Grossberg - 1991 - Journal of Symbolic Logic 56 (1):115-123.
    Basic results on the model theory of substructures of a fixed model are presented. The main point is to avoid the use of the compactness theorem, so this work can easily be applied to the model theory of L ω 1 ,ω and its relatives. Among other things we prove the following theorem: Let M be a model, and let λ be a cardinal satisfying λ |L(M)| = λ. If M does not have the ω-order property, then for every $A (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  14.  9
    On Chains of Relatively Saturated Submodels of a Model Without the Order Property.Rami Grossberg - 1991 - Journal of Symbolic Logic 56 (1):124-128.
    Let M be a given model with similarity type L = L(M), and let L' be any fragment of L |L(M)| +, ω of cardinality |L(M)|. We call $N \prec M L'$ -relatively saturated $\operatorname{iff}$ for every $B \subseteq N$ of cardinality less than | N | every L'-type over B which is realized in M is realized in M is realized in N. We discuss the existence of such submodels. The following are corollaries of the existence theorems. (1) If (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  15.  13
    The Equality S1 = D = R.Rami Grossberg, Alexei Kolesnikov, Ivan Tomašić & Monica Van Dieren - 2003 - Mathematical Logic Quarterly 49 (2):115-128.
    The new result of this paper is that for θ-stable we have S1[θ] = D[θ, L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the followingMain (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  16.  17
    A Downward Löwenheim-Skolem Theorem for Infinitary Theories Which Have the Unsuperstability Property.Rami Grossberg - 1988 - Journal of Symbolic Logic 53 (1):231-242.
    We present a downward Löwenheim-Skolem theorem which transfers downward formulas from L ∞,ω to L κ +, ω . The simplest instance is: Theorem 1. Let $\lambda > \kappa$ be infinite cardinals, and let L be a similarity type of cardinality κ at most. For every L-structure M of cardinality λ and every $X \subseteq M$ there exists a model $N \prec M$ containing the set X of power |X| · κ such that for every pair of finite sequences a, (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  17.  12
    Models with Second Order Properties in Successors of Singulars.Rami Grossberg - 1989 - Journal of Symbolic Logic 54 (1):122-137.
    Let L(Q) be first order logic with Keisler's quantifier, in the λ + interpretation (= the satisfaction is defined as follows: $M \models (\mathbf{Q}x)\varphi(x)$ means there are λ + many elements in M satisfying the formula φ(x)). Theorem 1. Let λ be a singular cardinal; assume □ λ and GCH. If T is a complete theory in L(Q) of cardinality at most λ, and p is an L(Q) 1-type so that T strongly omits $p (= p$ has no support, to (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  18.  12
    Local Order Property in Nonelementary Classes.Rami Grossberg & Olivier Lessmann - 2000 - Archive for Mathematical Logic 39 (6):439-457.
    . We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to generalize some of the results that were known in the case of local stability for the (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  19. On the Number of Nonisomorphic Models of an Infinitary Theory Which has the Infinitary Order Property. Part A.Rami Grossberg & Saharon Shelah - 1986 - Journal of Symbolic Logic 51 (2):302-322.
  20.  1
    Hodges Wilfrid. Building Models by Games. London Mathematical Society Student Texts, No. 2. Cambridge University Press, Cambridge Etc. 1985, Vi + 311 Pp. [REVIEW]Rami Grossberg - 1991 - Journal of Symbolic Logic 56 (2):752-753.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  21.  1
    Review: Wilfrid Hodges, Building Models by Games. [REVIEW]Rami Grossberg - 1991 - Journal of Symbolic Logic 56 (2):752-753.
  22. A Downward Löwenheim-Skolem Theorem for Infinitary Theories Which Have the Unsuperstability Property.Rami Grossberg - 1988 - Journal of Symbolic Logic 53 (1):231-242.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  23.  1
    Transfering Saturation, The Finite Cover Property, and Stability.John Baldwin, Rami Grossberg & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (2):678-684.
    $\underline{\text{Saturation is} -\text{transferable in} T}$ if and only if there is an expansion T$_1$ of T with $\mid T_1 \mid$ = $\mid T \mid$ such that if M is a $\mu$-saturated model of T$_1$ and $\mid M \mid \geq \kappa$ then the reduct M $\mid L$ is $\kappa$-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is - transferable or, \lambda$)-transferable for all $\lambda$. Further if for some $\mu \geq \mid T \mid, (...)
    Direct download  
     
    Export citation  
     
    My bibliography