Lindström's theorem

Source: Wikipedia, the free encyclopedia.

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[1] (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property and the (downward) Löwenheim–Skolem property.[2]

Lindström's theorem is perhaps the best known result of what later became known as abstract model theory,[3] the basic notion of which is an abstract logic;[4] the more general notion of an institution was later introduced, which advances from a set-theoretical notion of model to a category-theoretical one.[5] Lindström had previously obtained a similar result in studying first-order logics extended with Lindström quantifiers.[6]

Lindström's theorem has been extended to various other systems of logic, in particular modal logics by Johan van Benthem and Sebastian Enqvist.

Notes

  1. ISBN 0-387-90936-2
    page 43
  2. ISBN 1-4051-4575-7
    page 329
  3. ISBN 978-0-444-88054-3
    .
  4. ISBN 978-3-7643-7259-0
    .
  5. ISBN 978-0-19-853859-2
    .
  6. ^ Jouko Väänänen, Lindström's Theorem

References
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