Minimal bounded index subgroup for dependent theories

By Saharon Shelah. 2006

65 citations recorded by the source corpus.

For a dependent theory T, in C T for every type definable group G, the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/727f1f5adb5aad4ccccfebb7d0747197274d39ea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Artem Chernikov
2. Pierre Simon
3. Thomas Scanlon
4. Hans Adler
5. Itay Kaplan

In Mathematical Physics

1. Thomas Scanlon
2. Pierre Simon
3. Hans Adler
4. Itay Kaplan
5. Artem Chernikov

Citations in the corpus

• Artin-Schreier extensions in NIP and simple fields (2010, background): “By [25] (another presentation appears in [14, Proposition 6.”
• Definably amenable NIP groups (2015, result): “ls relatively to those infinitesimals, etc. — i.e., it satisfies a saturation condition: every small enough finitely consistent family of definable sets has non-empty intersection. It was shown by Shelah [She08] that any NIP group G(U)admits a unique maximal compact quotient denoted G/G00, which plays a”
• Introduction to theories without the independence property (2008, background): “Shelah then proved, without using measures, that this is true for all NIP theories [55].”
• Groups, measures, and the NIP (2006, unknown): “Our work may also overlap to some extent with recent papers of Shelah on theories without the independence property (for example [26], [27]).”