Kurt Gödel
![Gödel {{circa}} 1926](https://upload.wikimedia.org/wikipedia/commons/4/42/Kurt_g%C3%B6del.jpg)
Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two years later, in 1931. The first incompleteness theorem states that for any ω-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example, Peano arithmetic), there are true propositions about the natural numbers that can be neither proved nor disproved from the axioms. To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers. The second incompleteness theorem, which follows from the first, states that the system cannot prove its own consistency.
Gödel also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted Zermelo–Fraenkel set theory, assuming that its axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic. Provided by Wikipedia
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Published: 1850
Superior document: Enthalten in Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften Wien : Aus der K.K. Hof- und Staatsdruckerei, 1850 5. Band (Jahrgang 1850), 1. Heft (Juni), Seite 1 [=3]-4
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Published: [2023]
Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2024 Part 1
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Published: [2016]
Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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Published: [2012]
Superior document: Title is part of eBook package: De Gruyter DGBA Literary and Cultural Studies 2000 - 2014
Links: Get full text; Get full text; Cover
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Published: [2020]
Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2020 Part 1
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Published: [2015]
Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2015 Part 1
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Published: [2021]
Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2021 Part 1
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Published: [2019]
Superior document: Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019
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Published: [2023]
Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
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Published: 1985
Superior document: Collection d'études musicologiques 69
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Published: 2015.
Superior document: Theologische Bibliothek Topelmann, Band 171
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Other Authors:
“...Godel, Robert...”
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Published: 1987
Superior document: History of logic 4
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Published: 1995-
Links: Inhaltsverzeichnis
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Published: 2012.
Superior document: Laboratorium Aufklärung; volume10
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“...Kurt-Gödel-Gesellschaft...”
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Published: 2010.
Superior document: Laboratorium Aufklärung; volume4
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Published: 2016
Superior document: Acta Historica Leopoldina Nummer 68
Links: Inhaltsverzeichnis; Inhaltstext