Journal
JOURNAL OF MATHEMATICAL LOGIC
Volume 23, Issue 3, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219061322500271
Keywords
Hyperimaginaries; approximate subgroups; connected components; Lie models; stabilizer theorems
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The aim of this paper is to extend and improve two of the main model-theoretic results by Hrushovski in the context of piecewise hyperdefinable sets, namely the existence of Lie models and the Stabilizer Theorem. This study also includes a systematic investigation of the structure of piecewise hyperdefinable sets, particularly focusing on their logic topologies.
The aim of this paper is to generalize and improve two of the main model-theoretic results of Stable group theory and approximate subgroups by Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence of Lie models. The second one is the Stabilizer Theorem. In the process, a systematic study of the structure of piecewise hyperdefinable sets is developed. In particular, we show the most significant properties of their logic topologies.
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