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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Partially supported by grants MTM 2011-26840 of Spanish Ministry of Economy and Competitiveness and 2009SGR-187 of Catalan Government.
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Casanovas, E., Potier, J. Normal hyperimaginaries. Arch. Math. Logic 53, 583–591 (2014). https://doi.org/10.1007/s00153-014-0382-y
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DOI: https://doi.org/10.1007/s00153-014-0382-y
Keywords
- Bounded hyperimaginaries
- Finitary hyperimaginaries
- Peter–Weyl theorem
- Kim-Pillay equivalence relation
- Types over hyperimaginaries