English

Homogenizable structures and model completeness

Logic 2018-02-09 v2

Abstract

A homogenizable structure M\mathcal{M} is a structure where we may add a finite amount of new relational symbols to represent some \emptyset-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an ω\omega-categorical model-complete structure to be homogenizable.

Keywords

Cite

@article{arxiv.1601.07304,
  title  = {Homogenizable structures and model completeness},
  author = {Ove Ahlman},
  journal= {arXiv preprint arXiv:1601.07304},
  year   = {2018}
}

Comments

20 pages. Proposition 3.4 is removed from the lates version since the proof contained an error, however no other results depend on it so the rest of the paper remain consistent

R2 v1 2026-06-22T12:37:38.442Z