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pro vyhledávání: '"Grossberg, Rami"'
Autor:
Grossberg, Rami, Mazari-Armida, Marcos
We introduce and study simple and supersimple independence relations in the context of AECs with a monster model. $Theorem$: Let $K$ be an AEC with a monster model. - If $K$ has a simple independence relation, then $K$ does not have the 2-tree proper
Externí odkaz:
http://arxiv.org/abs/2003.02705
Publikováno v:
Annals of Pure and Applied Logic 168 (2017), no. 7, 1383-1395
Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for a certain independence relation called nonsplitting. We g
Externí odkaz:
http://arxiv.org/abs/1609.07101
Publikováno v:
Journal of Pure and Applied Algebra 220 (2016), no. 9, 3048-3066
We introduce $\mu$-Abstract Elementary Classes ($\mu$-AECs) as a broad framework for model theory that includes complete boolean algebras and Dirichlet series, and begin to develop their classification theory. Moreover, we note that $\mu$-AECs corres
Externí odkaz:
http://arxiv.org/abs/1509.07377
Autor:
Grossberg, Rami, Vasey, Sebastien
Publikováno v:
The Journal of Symbolic Logic 82 (2017), no. 4, 1387-1408
In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the
Externí odkaz:
http://arxiv.org/abs/1507.04223
We prove: Main Theorem: Let $\mathcal{K}$ be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality $\mu$. Let $\mu$ be a cardinal above the the L\"owenheim-Skolem number of t
Externí odkaz:
http://arxiv.org/abs/1507.02118
Publikováno v:
Annals of Pure and Applied Logic 167 (2016), no. 7, 590-613
Boney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and local cha
Externí odkaz:
http://arxiv.org/abs/1404.1494
Autor:
Boney, Will, Grossberg, Rami
We develop a notion of forking for Galois-types in the context of Abstract Elementary Classes (AECs). Under the hypotheses that an AEC $K$ is tame, type-short, and failure of an order-property, we consider {\bf Definition.} Let $M_0 \prec N$ be model
Externí odkaz:
http://arxiv.org/abs/1306.6562
Autor:
Grossberg, Rami, VanDieren, Monica
Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is \chi-tame. If K is categorical in some \lambda^+ >LS(K) then it is categorical in all \m
Externí odkaz:
http://arxiv.org/abs/math/0510004
Autor:
Grossberg, Rami, Lessmann, Olivier
Publikováno v:
Contemporary Mathematics, Vol 380, (2005), pp. 73--108
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap
Externí odkaz:
http://arxiv.org/abs/math/0509707
Autor:
Grossberg, Rami, VanDieren, Monica
We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper we explore stability results in this context. We assume that $\
Externí odkaz:
http://arxiv.org/abs/math/0509535