Annals of Pure and Applied Logic 131 (1-3):227-261 (2005)

Abstract
The main topic of this paper is the investigation of generalized amalgamation properties for simple theories. That is, we are trying to answer the question of when a simple theory has the property of n-dimensional amalgamation, where two-dimensional amalgamation is the Independence Theorem for simple theories. We develop the notions of strong n-simplicity and n-simplicity for 1≤n≤ω, where both “1-simple” and “strongly 1-simple” are the same as “simple”. For strong n-simplicity, we present examples of simple unstable theories in each subclass and prove a characteristic property of strong n-simplicity in terms of strong n-dividing, a strengthening of the dependence relation called dividing in simple theories. We prove a strong three-dimensional amalgamation property for strongly 2-simple theories, and, under an additional assumption, a strong -dimensional amalgamation property for strongly n-simple theories. In the last section of the paper we comment on why strong n-simplicity is called strong
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DOI 10.1016/j.apal.2004.06.001
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References found in this work BETA

Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.
Simplicity, and Stability in There.Byunghan Kim - 2001 - Journal of Symbolic Logic 66 (2):822-836.
A Primer of Simple Theories.Rami Grossberg, José Iovino & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (6):541-580.
Lascar Strong Types in Some Simple Theories.Steven Buechler - 1999 - Journal of Symbolic Logic 64 (2):817-824.
Definability in Low Simple Theories.Ziv Shami - 2000 - Journal of Symbolic Logic 65 (4):1481-1490.

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Citations of this work BETA

Generalized Amalgamation and N -Simplicity.Byunghan Kim, Alexei S. Kolesnikov & Akito Tsuboi - 2008 - Annals of Pure and Applied Logic 155 (2):97-114.
Failure of N -Uniqueness: A Family of Examples.Elisabetta Pastori & Pablo Spiga - 2011 - Mathematical Logic Quarterly 57 (2):133-148.
Independence and the Finite Submodel Property.Vera Koponen - 2009 - Annals of Pure and Applied Logic 158 (1-2):58-79.

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