On the downward Löwenheim-Skolem Theorem for elementary submodels

Published 6 Jun 2024 in math.LO | (2406.03860v1)

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.

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Matthias Kunik

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