Leopold Löwenheim
Learn about this topic in these articles:
metalogicThe Löwenheim-Skolem theoremâŠtheorem (1915, 1920), named after Leopold Löwenheim, a German schoolteacher, and Skolem, which says that if a sentence (or a formal system) has any model, it has a countable or enumerable model (i.e., a model whose members can be matched with the positive integers). In the most direct method ofâŠ
Read MoreâŠtheorem (1915, 1920), named after Leopold Löwenheim, a German schoolteacher, and Skolem, which says that if a sentence (or a formal system) has any model, it has a countable or enumerable model (i.e., a model whose members can be matched with the positive integers). In the most direct method ofâŠ
Read More- metalogicSatisfaction of a theory by a structure: finite and infinite models
âŠmathematician Ernst Schröder and in Löwenheim (in particular, in his paper of 1915). The basic tools and results achieved in model theoryâsuch as the Löwenheim-Skolem theorem, the completeness theorem of elementary logic, and Skolemâs construction of nonstandard models of arithmeticâwere developed during the period from 1915 to 1933. A moreâŠ
Read MoreâŠmathematician Ernst Schröder and in Löwenheim (in particular, in his paper of 1915). The basic tools and results achieved in model theoryâsuch as the Löwenheim-Skolem theorem, the completeness theorem of elementary logic, and Skolemâs construction of nonstandard models of arithmeticâwere developed during the period from 1915 to 1933. A moreâŠ
Read More 
history of logicCompletenessâŠshown, by the German logician Leopold Löwenheim and the Norwegian mathematician Thoralf Skolem, that first-order axiom systems cannot be complete in this Hilbertian sense. The theorem that bears their namesâthe Löwenheim-Skolem theoremâhas two parts. First, if a first-order proposition or finite axiom system has any models, it has countable models.âŠ
Read MoreâŠshown, by the German logician Leopold Löwenheim and the Norwegian mathematician Thoralf Skolem, that first-order axiom systems cannot be complete in this Hilbertian sense. The theorem that bears their namesâthe Löwenheim-Skolem theoremâhas two parts. First, if a first-order proposition or finite axiom system has any models, it has countable models.âŠ
Read More