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In mathematical logic the Löwenheim number of an abstract logic is the smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds.〔Zhang 2002 page 77〕 They are named after Leopold Löwenheim, who proved that these exist for a very broad class of logics. == Abstract logic == An abstract logic, for the purpose of Löwenheim numbers, consists of: * A collection of "sentences"; * A collection of "models", each of which is assigned a cardinality; * A relation between sentences and models that says that a certain sentence is "satisfied" by a particular model. The theorem does not require any particular properties of the sentences or models, or of the satisfaction relation, and they may not be the same as in ordinary first-order logic. It thus applies to a very broad collection of logics, including first-order logic, higher-order logics, and infinitary logics. 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「Löwenheim number」の詳細全文を読む スポンサード リンク
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