Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories.
Teorema ketaklengkapan Gödel (bahasa Inggris: Gödel's incompleteness theoremscode: en is deprecated ) adalah dua teorema logika matematika yang menetapkan batasan (limitation) inheren dari semua kecuali sistem aksiomatik yang paling trivial yang mampu mengerjakan aritmetika.
These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.
Teorema-teorema ini, dibuktikan oleh Kurt Gödel pada tahun 1931, penting baik dalam logika matematika maupun dalam filsafat matematika.
Gödel's first incompleteness theorem first appeared as "Theorem VI" in Gödel's 1931 paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I".
Teorema ketidaklengkapan Gödel yang pertama pertama kali muncul sebagai "Teorema VI" dalam makalah Gödel pada tahun 1931 berjudul "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I." Teorema ini ditulis dalam matematika formal yang sangat teknis.
After Gödel published his proof of the completeness theorem as his doctoral thesis in 1929, he turned to a second problem for his habilitation.
Setelah Gödel memublikasikan buktinya mengenai teorema kelengkapan sebagai tesis doktoralnya pada tahun 1929, ia beralih kepada problem kedua untuk habilitasinya.
His original goal was to obtain a positive solution to Hilbert's second problem.
Tujuan asalnya adalah untuk memperoleh pemecahan positif dari problem kedua Hilbert (Dawson 1997, p. 63).
At the time, theories of natural numbers and real numbers similar to second-order arithmetic were known as "analysis", while theories of natural numbers alone were known as "arithmetic".
Pada saat itu, teori-teori bilangan asli dan bilangan real yang mirip dengan aritmetika order kedua dikenal sebagai "analisis", sedangkan teori-teori bilangan asli saja dikenal sebagai "aritmetika".
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Terjemahan makalah Gödel ke dalam bahasa Inggris semasa hidupnya
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