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