# Kurt Gödel , ‘ Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I ’ ( 1931 )

@inproceedings{Zach2003KurtG, title={Kurt G{\"o}del , ‘ {\"U}ber formal unentscheidbare S{\"a}tze der Principia mathematica und verwandter Systeme I ’ ( 1931 )}, author={Richard Zach}, year={2003} }

First publication: Monatshefte f ür Mathematik und Physik , 37, 173–198 Reprints:S. Feferman et al., eds., Kurt Gödel. Collected Works. Volume I: Publications 1929–1936. New York: Oxford University Press, 1986, pp. 116–195. Translations:English translations: ‘On formally undecidable propositions of Principia mathematicaand related systems I.’ Translation by B. Meltzer, On Formally Undecidable Propositions of Principia Mathematica and Related Systems , Edinburgh: Oliver and Boyd, 1962… Expand

#### 9 Citations

Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos

- Computer Science, Medicine
- Physics of life reviews
- 2019

The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecIDability. Expand

Sailing Routes in the World of Computation

- Computer Science
- Lecture Notes in Computer Science
- 2018

The tutorial focuses on computably enumerable (c.e.) structures, a class that properly extends the class of all computable structures and the interplay between important constructions, concepts, and results in computability, universal algebra, and algebra. Expand

DNA coding and G\"odel numbering.

- Biology
- 2019

Inspired by the work of Kurt Godel, the DNA strand is attached to each DNA strand a Godel's number, a product of prime numbers raised to appropriate powers, to specify the presence of traces of non-random dynamics. Expand

On formally undecidable propositions of Zermelo-Fraenkel set theory

- Mathematics
- 2013

We present a demonstration of the Gödel’s incompleteness phenomenon in the formal first-order axiomatization of the Zermelo-Fraenkel axioms (ZF) of set theory following the methods displayed in… Expand

Syntax Evolution: Problems and Recursion

- Computer Science
- ArXiv
- 2015

This work explains the anomaly of syntax by postulating that syntax and problem solving co-evolved in humans towards Turing completeness, and finds firstly that semantics is not sufficient and that syntax is necessary to represent problems and that full problem solving requires a functional semantics on an infinite tree-structured syntax. Expand

15-424 : Foundations of Cyber-Physical Systems Lecture Notes on Ghosts & Differential Ghosts

- 2013

Lecture 10 on Differential Equations & Differential Invariants and Lecture 11 on Differential Equations & Proofs equipped us with powerful tools for proving properties of differential equations… Expand

How Hilbert’s Attempt to Unify Gravitation and Electromagnetism Failed Completely, and a Plausible Resolution

- Mathematics
- 2018

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of… Expand

A Plausible Resolution to Hilbert’s Failed Attempt to Unify Gravitation & Electromagnetism

- Mathematics
- 2018

In this paper, we explore the reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed and outline a plausible resolution of this problem. The latter is based… Expand

Electron Model Based on Helmholtz’s Electron Vortex Theory & Kolmogorov’s Theory of Turbulence

- Physics
- 2018

In this paper, we explore a new electron model based on Helmholtz’s electron vortex and Kolmogorov theory of turbulence. We also discuss a new model of origination of charge and matter.

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What were the earliest reactions to Godel's incompleteness theorems? After a brief summary of previous work in this area I analyse, by means of unpublished archival material, the first reactions in… Expand

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Jakina da Whiteheadek eta Russellek logika eta matematika eraiki dutela ageriko zenbait proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikako… Expand