- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- NTP_2 groups with f-generics and PRC fields
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
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
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2018-10-17T10:12
|
| 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.
|
| Extent |
40.0
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: Universidad de Costa Rica
|
| Series | |
| Date Available |
2019-04-16
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0378231
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Postdoctoral
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International