Title: The Löwenheim–Skolem Theorem and the Compactness Theorem
Abstract: This chapter treats consequences of the Completeness Theorem, thus establishing the beginnings of the model theory of first-order logic: The (downward and upward) Löwenheim-Skolem theorems and the Compactness Theorem are proved. As a consequence, several results on the limits of the expressive power of first-order logic are presented. As a positive aspect of these limits the existence of nonstandard models is shown.
Publication Year: 2021
Publication Date: 2021-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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