5 resultados para Logic, Modern

em Boston University Digital Common


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http://www.archive.org/details/amodernpioneerin00grifuoft

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http://www.archive.org/details/modernreligiousm025064mbp

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http://www.archive.org/details/thoughtsfrommode00walsuoft

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http://www.archive.org/details/makingofmodernmi011868mbp

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We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.