English

On the downward L\"owenheim-Skolem Theorem for elementary submodels

Logic 2026-03-03 v2

Abstract

We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications due to a general syntax used in the formal systems. For our models we present a new proof of the downward L\"owenheim-Skolem Theorem for elementary submodels.

Keywords

Cite

@article{arxiv.2406.03860,
  title  = {On the downward L\"owenheim-Skolem Theorem for elementary submodels},
  author = {Matthias Kunik},
  journal= {arXiv preprint arXiv:2406.03860},
  year   = {2026}
}

Comments

We have corrected some typos and improved our notation. 28 pages