Lindström's theorem
Template:Short description 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
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- ↑ In the sense of Heinz-Dieter Ebbinghaus Extended logics: the general framework in K. J. Barwise and S. Feferman, editors, Model-theoretic logics, 1985 Template:Isbn page 43
- ↑ A companion to philosophical logic by Dale Jacquette 2005 Template:Isbn page 329
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- ↑ Jouko Väänänen, Lindström's Theorem
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References
- Per Lindström, "On Extensions of Elementary Logic", Theoria 35, 1969, 1–11. Script error: No such module "CS1 identifiers".
- Johan van Benthem, "A New Modal Lindström Theorem", Logica Universalis 1, 2007, 125–128. Script error: No such module "CS1 identifiers".
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- Sebastian Enqvist, "A General Lindström Theorem for Some Normal Modal Logics", Logica Universalis 7, 2013, 233–264. Script error: No such module "CS1 identifiers".
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- Shawn Hedman, A first course in logic: an introduction to model theory, proof theory, computability, and complexity, Oxford University Press, 2004, Template:Isbn, section 9.4
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