Kurt Godel - Academia.edu (original) (raw)

Kurt Godel

Short and to the point, polymath in the sciences and mathematics, funny and easy going, deep thinking about UltraDeep Time!

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Papers by Kurt Godel

Research paper thumbnail of Rotating Universes in General Relativity Theory

General Relativity and Gravitation, 2000

Research paper thumbnail of On the length of proofs

Research paper thumbnail of Mathematical Logic and Its Applications

Research paper thumbnail of Large cardinals and definable well-orders on the universe

The Journal of Symbolic Logic, 2009

We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while... more We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle , at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

Research paper thumbnail of On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The American Mathematical Monthly, 1966

Gödel's famous proof [2, 1] is highly interesting, but may be hard to understand. Some of this di... more Gödel's famous proof [2, 1] is highly interesting, but may be hard to understand. Some of this difficulty is due to the fact that the notation used by Gödel has been largely replaced by other notation. Some of this difficulty is due to the fact that while Gödel's formulations are concise, they sometimes require the readers to make up their own interpretations for formulae, or to keep definitions in mind that may not seem mnemonic to them. This document is a translation of a large part of Gödel's proof. The translation happens on three levels: • from German to English • from Gödel's notation to more common mathematical symbols • from paper to hyper-text Hyper-text and colors are used as follows: definitions take place in blue italics, like this: defined term. Wherever the defined term is used, we have a red hyper-link to the place in the text where the term was first defined, like this: defined term. Furthermore, each defined term appears in the clickable index at the end of this document.

Research paper thumbnail of How Godel Transformed Set Theory

Notices of the American Mathematical Society, 2006

Research paper thumbnail of Rotating Universes in General Relativity Theory

General Relativity and Gravitation, 2000

Research paper thumbnail of On the length of proofs

Research paper thumbnail of Mathematical Logic and Its Applications

Research paper thumbnail of Large cardinals and definable well-orders on the universe

The Journal of Symbolic Logic, 2009

We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while... more We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle , at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

Research paper thumbnail of On Formally Undecidable Propositions of Principia Mathematica and Related Systems

The American Mathematical Monthly, 1966

Gödel's famous proof [2, 1] is highly interesting, but may be hard to understand. Some of this di... more Gödel's famous proof [2, 1] is highly interesting, but may be hard to understand. Some of this difficulty is due to the fact that the notation used by Gödel has been largely replaced by other notation. Some of this difficulty is due to the fact that while Gödel's formulations are concise, they sometimes require the readers to make up their own interpretations for formulae, or to keep definitions in mind that may not seem mnemonic to them. This document is a translation of a large part of Gödel's proof. The translation happens on three levels: • from German to English • from Gödel's notation to more common mathematical symbols • from paper to hyper-text Hyper-text and colors are used as follows: definitions take place in blue italics, like this: defined term. Wherever the defined term is used, we have a red hyper-link to the place in the text where the term was first defined, like this: defined term. Furthermore, each defined term appears in the clickable index at the end of this document.

Research paper thumbnail of How Godel Transformed Set Theory

Notices of the American Mathematical Society, 2006

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