English

Generic derivations on algebraically bounded structures

Logic 2024-11-14 v4 Commutative Algebra

Abstract

Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by TδT^{\delta}, has a model completion. Additionally, we prove that if the theory T is stable/NIP then the model completion of TδT^{\delta} is also stable/NIP. Similar results hold for the theory with several derivations, either commuting or non-commuting.

Keywords

Cite

@article{arxiv.2310.20511,
  title  = {Generic derivations on algebraically bounded structures},
  author = {Fornasiero Antongiulio and Terzo Giuseppina},
  journal= {arXiv preprint arXiv:2310.20511},
  year   = {2024}
}

Comments

Changes: Addded or updated the following references: [FT24] [LM16] [LT24], [JY23b] Corrected the text of Fact 2. Minor typos