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Fixpunktssatsen Fixpunkttheorem Diagonal lemma Lema da diagonal 對角線引理
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Na lógica matemática, o lema da diagonal ou teorema do ponto fixo estabelece a existência de sentenças em certas teorias formais dos números naturais - especificamente as teorias que são fortes o suficiente para representar todas as . As sentenças, cuja existência é garantida pelo lema da diagonal podem então, por sua vez, ser usadas para provar resultados fundamentalmente limitativos, tais como teorema da incompletude de Gödel e o teorema da indefinibilidade de Tarski. Das Fixpunkttheorem (auch Fixpunktsatz oder Diagonalisierungslemma) ist ein Satz in der mathematischen Logik zur Beschreibung selbstreferenzieller Aussagen in formalen Theorien. Es wurde von Kurt Gödel 1931 zur Konstruktion seines Beweises der Unvollständigkeit logischer Systeme, die so ausdrucksstark sind, dass man damit die natürlichen Zahlen axiomatisieren kann, verwendet und damit implizit bewiesen, allerdings nicht explizit unter diesem Namen erwähnt. Das Theorem leitet sich von dem Diagonalisierungslemma ab, das so in Anlehnung an das Diagonalisierungsargument von Georg Cantor genannt wird. Låt vara Peanos aritmetik. Fixpunktssatsen för är följande påstående: För varje formel finns en sats sådan att Fixpunktssatsen används flitigt i metalogiska resonemang, till exempel i konstruktionen av gödelsatser, rossersatser och henkinsatser. 對角線引理(diagonal lemma),又稱為不動點定理(fixed point theorem)。在數理邏輯中,對角線引理表明了自然數的形式理論中自指句子的存在——尤其是那些強到足以表示所有可計算函數的形式理論。 由對角線引理確立其存在的句子,將可用於證明一些邏輯的基礎限制,例如:哥德爾不完備定理或塔斯基不可定義定理。 In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem.
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Na lógica matemática, o lema da diagonal ou teorema do ponto fixo estabelece a existência de sentenças em certas teorias formais dos números naturais - especificamente as teorias que são fortes o suficiente para representar todas as . As sentenças, cuja existência é garantida pelo lema da diagonal podem então, por sua vez, ser usadas para provar resultados fundamentalmente limitativos, tais como teorema da incompletude de Gödel e o teorema da indefinibilidade de Tarski. 對角線引理(diagonal lemma),又稱為不動點定理(fixed point theorem)。在數理邏輯中,對角線引理表明了自然數的形式理論中自指句子的存在——尤其是那些強到足以表示所有可計算函數的形式理論。 由對角線引理確立其存在的句子,將可用於證明一些邏輯的基礎限制,例如:哥德爾不完備定理或塔斯基不可定義定理。 Låt vara Peanos aritmetik. Fixpunktssatsen för är följande påstående: För varje formel finns en sats sådan att Fixpunktssatsen används flitigt i metalogiska resonemang, till exempel i konstruktionen av gödelsatser, rossersatser och henkinsatser. In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem. Das Fixpunkttheorem (auch Fixpunktsatz oder Diagonalisierungslemma) ist ein Satz in der mathematischen Logik zur Beschreibung selbstreferenzieller Aussagen in formalen Theorien. Es wurde von Kurt Gödel 1931 zur Konstruktion seines Beweises der Unvollständigkeit logischer Systeme, die so ausdrucksstark sind, dass man damit die natürlichen Zahlen axiomatisieren kann, verwendet und damit implizit bewiesen, allerdings nicht explizit unter diesem Namen erwähnt. Das Theorem leitet sich von dem Diagonalisierungslemma ab, das so in Anlehnung an das Diagonalisierungsargument von Georg Cantor genannt wird.
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