Normal hyperimaginaries

Enrique Casanovas; Joris Potier

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arXiv · 1112.2049

Normal hyperimaginaries

Enrique Casanovas·Joris Potier

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Abstract

We introduce the notion of normal hyperimaginary and we develop its basic theory. We present a new proof of Lascar-Pillay's theorem on bounded hyperimaginaries based on properties of normal hyperimaginaries. However, the use of Peter-Weyl's 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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BibTeX RIS

Enrique Casanovas, Joris Potier. 2013-12-05. Normal hyperimaginaries. https://arxiv.org/abs/1112.2049

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