Lindström's theorem [SEP] named after
Lindström's theorem
In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the "strongest logic" (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property and the (downward) Löwenheim–Skolem property.
Lindström's theorem is perhaps the best known result of what later became known as abstract model theory, the basic notion of which is an abstract logic; the more general notion
Abstract model theory
In mathematical logic, abstract model theory is a generalization of model theory which studies the general properties of extensions of first-order logic and their models.
Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. The starting point for the study of abstract models, which resulted in good examples was Lindström's theorem.
In 1974 Jon Barwise provided an axiomatization of abstract model theory.
See also.
- Lindström's theorem