The Amalgamation Property for automorphisms of ordered abelian groups
arXiv:2209.03944 · doi:10.1090/tran/9217
Abstract
We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is NIP in the sense of positive logic, and initiate a development of the latter framework. As byproducts of the proof, we obtain a generalised version of the Hahn Embedding Theorem which allows to lift each automorphism of an ordered abelian group to one of an ordered real vector space, and we show that, on existentially closed structures, linear combinations of iterates of the automorphism have the Intermediate Value Property.
We have corrected the proof of Proposition 2.8
References in corpus (9)
- Model Theory and Machine Learning
- Kim-independence in positive logic
- Existentially Closed Exponential Fields
- Spaces of Types in Positive Model Theory
- Dividing Lines between Positive Theories
- Linearly ordered sets with only one operator have the amalgamation property
- The automorphism group of a valued field of generalised formal power series
- Maximal stable quotients of invariant types in NIP theories
- Type space functors and interpretations in positive logic