Boissonneau, Blaise: Combinatorial complexity in henselian valued fields : pushing Anscombe-Jahnke up the ladder. 2022
Inhalt
- Introduction
- Combinatorial complexity
- Complexity of fields and Artin-Schreier extensions
- Valued fields
- Complexity of henselian valued fields
- Algebraic extensions of Qp
- Algebra and Model Theory of Valued Fields
- Valuation theory
- Henselianity
- Model theory of valued fields
- Ordered abelian groups
- Languages of valued fields
- Algebraically closed valued fields
- The AKE principle
- Definability of valuations
- Artin-Schreier Extensions & Combinatorial Complexity
- Stable fields
- NIP fields
- The independence property
- NIP fields
- Baldwin-Saxl condition for NIP formulas
- Artin-Schreier closure and local NIPity
- Lifting
- Explicit Shelah's conjecture
- Consequences on other conjectures
- dp-finite fields
- NIPn fields
- The n-independence property
- NIPn fields
- Baldwin-Saxl-Hempel's condition for NIPn formulas
- Artin-Schreier closure of NIPn fields
- Lifting
- Simple fields
- NTP2 fields
- NIPn Henselian Valued Fields
- Combinatorial Complexity in Algebraic Extensions of Qp
- Definability of vp in algebraic extensions of Qp
- NIPn-ity of algebraic extensions of Qp
- State of art for some complexity classes
- Appendix