Normal hyperimaginaries

Archive for Mathematical Logic 53 (5-6):583-591 (2014)

Abstract

We introduce the notion of normal hyperimaginary and we develop its basic theory. We present a new proof of the Lascar-Pillay theorem on bounded hyperimaginaries based on properties of normal hyperimaginaries. However, the use of the Peter–Weyl theorem on the structure of compact Hausdorff groups is not completely eliminated from the proof. In the second part, we show that all closed sets in Kim-Pillay spaces are equivalent to hyperimaginaries and we use this to introduce an approximation of φ-types for bounded hyperimaginaries.

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References found in this work

Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.

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Citations of this work

The Lascar Group and the Strong Types of Hyperimaginaries.Byunghan Kim - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):497-507.

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