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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'' 〔In the sense of Heinz-Dieter Ebbinghaus ''Extended logics: the general framework'' in K. J. Barwise and S. Feferman, editors, ''Model-theoretic logics'', 1985 ISBN 0-387-90936-2 page 43〕 (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property and the (downward) Löwenheim–Skolem property.〔''A companion to philosophical logic'' by Dale Jacquette 2005 ISBN 1-4051-4575-7 page 329〕 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 of an institution was later introduced, which advances from a set-theoretical notion of model to a category theoretical one. Lindström had previously obtained a similar result in studying first-order logics extended with Lindström quantifiers.〔Jouko Väänänen, (Lindström's Theorem )〕 Lindström's theorem has been extended to various other systems of logic in particular modal logics by Johan van Benthem and Sebastian Enqvist. ==Notes== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lindström's theorem」の詳細全文を読む スポンサード リンク
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