Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Dated November 17, 1930, it was originally published in German in the 1931 volume of Monatshefte für Mathematik. Several English translations have appeared in print, and the paper has been included in two collections of classic m...
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Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Dated November 17, 1930, it was originally published in German in the 1931 volume of Monatshefte für Mathematik. Several English translations have appeared in print, and the paper has been included in two collections of classic mathematical logic papers. The paper is famous for the theorems it contains, which have many implications for consistency proofs in mathematics, and for the techniques that Gödel invented to prove these theorems.
The main results established are Gödel's first and second incompleteness theorems, which have had an enormous impact on the field of mathematical logic. These appear as theorems VI and XI, respectively, in the paper.
In order to prove these results, Gödel introduced in this paper a method now known as Gödel numbering. In this method,...
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