On the downward L\"owenheim-Skolem Theorem for elementary submodels
Matthias Kunik
TL;DR
This paper introduces an algebraic approach to model theory through a new definition of models based on substitution, and provides a novel proof of the downward Löwenheim-Skolem theorem for elementary submodels.
Contribution
It presents a new algebraic framework for models in formal systems and offers a fresh proof of the downward Löwenheim-Skolem theorem.
Findings
New algebraic model definition based on substitution
Purely algebraic proof of the downward Löwenheim-Skolem theorem
Applicable to formal systems with general syntax
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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Taxonomy
TopicsMathematics and Applications · Advanced Numerical Analysis Techniques · Advanced Optimization Algorithms Research