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NTP_2 groups with f-generics and PRC fields Montenegro, Samaria
Description
This is a joint work with Alf Onshuus and Pierre Simon. In this talk we focus on groups with f-generic types definable in NTP2 theories. In particular we study the case of bounded PRC fields. PRC fields were introduced by Prestel and Basarav as a generalization of real closed fields and pseudo algebraically closed fields, where we admit having several orders. We know that the complete theory of a bounded PRC field is NTP2 and we have a good description of forking. We use some alternative versions of Hrushovskiâ s â Stabilizer Theoremâ to describe the definable groups with f generics in PRC fields. The main theorem is that such a group is isogeneous with a finite index subgroup of a quantifier-free definable groups. In fact, the latter group admits a definable covering by multi-cells on which the group operation is algebraic. This generalizes similar results proved by Hrushovski and Pillay for (not necessarily f-generic) groups definable in both pseudo finite fields and real closed fields.
Item Metadata
Title |
NTP_2 groups with f-generics and PRC fields
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-10-17T10:12
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Description |
This is a joint work with Alf Onshuus and Pierre Simon.
In this talk we focus on groups with f-generic types definable in NTP2 theories. In particular we study the case of bounded PRC fields.
PRC fields were introduced by Prestel and Basarav as a generalization of real closed fields and pseudo algebraically closed fields, where we admit having several orders. We know that the complete theory of a bounded PRC field is NTP2 and we have a good description of forking.
We use some alternative versions of Hrushovskiâ s â Stabilizer Theoremâ to describe the definable groups with f generics in PRC fields. The main theorem is that such a group is isogeneous with a finite index subgroup of a quantifier-free definable groups. In fact, the latter group admits a definable covering by multi-cells on which the group operation is algebraic. This generalizes similar results proved by Hrushovski and Pillay for (not necessarily f-generic) groups definable in both pseudo finite fields and real closed fields.
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Extent |
40.0
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universidad de Costa Rica
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Series | |
Date Available |
2019-04-16
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0378231
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International