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The Birth of Model Theory by Calixto Badesa

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Chapter Five

Preliminaries to Löwenheim's Theorem

5.1 INDICES AND ELEMENTS

Löwenheim uses the word “index” to refer both to variables of the formal language and to elements of the domain. Bearing in mind the fact that no distinction was made at that time between object language and metalanguage, and also that the same letters are used as variables of the formal language and as metalinguistic variables ranging over elements of the domain, a certain degree of inaccuracy is understandable. If the ambiguity amounted to this alone, there would be no need for any comment, since today we make all these distinctions and we are often not as careful as we might be. However, in “Über Möglichkeiten” Löwenheim seems to identify the domain with the set of ...

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