Simplicity in compact abstract theories

Journal of Mathematical Logic 3 (02):163-191 (2003)
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Abstract

We continue [2], developing simplicity in the framework of compact abstract theories. Due to the generality of the context we need to introduce definitions which differ somewhat from the ones use in first order theories. With these modified tools we obtain more or less classical behaviour: simplicity is characterized by the existence of a certain notion of independence, stability is characterized by simplicity and bounded multiplicity, and hyperimaginary canonical bases exist.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Positive model theory and compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
Definability in low simple theories.Ziv Shami - 2000 - Journal of Symbolic Logic 65 (4):1481-1490.
Definability and definable groups in simple theories.Anand Pillay - 1998 - Journal of Symbolic Logic 63 (3):788-796.

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