Corpus ID: 15567546

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

  title={Kurt G{\"o}del , ‘ {\"U}ber formal unentscheidbare S{\"a}tze der Principia mathematica und verwandter Systeme I ’ ( 1931 )},
  author={Richard Zach},
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
Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos
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
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.
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
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 inExpand
Syntax Evolution: Problems and Recursion
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
Lecture 10 on Differential Equations & Differential Invariants and Lecture 11 on Differential Equations & Proofs equipped us with powerful tools for proving properties of differential equationsExpand
How Hilbert’s Attempt to Unify Gravitation and Electromagnetism Failed Completely, and a Plausible Resolution
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 ofExpand
A Plausible Resolution to Hilbert’s Failed Attempt to Unify Gravitation & Electromagnetism
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 basedExpand
Electron Model Based on Helmholtz’s Electron Vortex Theory & Kolmogorov’s Theory of Turbulence
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.


The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis.
  • K. Gödel
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1938
Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century and ranked higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. Expand
The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program
  • R. Zach
  • Mathematics, Computer Science
  • Synthese
  • 2004
The paper traces the development of the ``simultaneous development of logic and mathematics'' through the ∈-notation and provides an analysis of Ackermann's consistency proofs for primitive recursive arithmetic and for the first comprehensive mathematical system, the latter using thesubstitution method. Expand
Reflections on Kurt Gödel
Newton/Descartes. Einstein/Gdel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gdel was indisputably one of the greatest thinkersExpand
Grundlagen der Mathematik
AbstractTHAT the foundations of mathematics are A important is a proposition which will find few opponents, for the science of mathematics is commonly regarded as man's securest intellectualExpand
Extensions of Some Theorems of Gödel and Church
  • J. Rosser
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1936
It is proved that simple consistency implies the existence of undecidable propositions and the non-existence of an Entscheidungsverfahren by a strengthening of Godel's Satz VI and Kleene's Theorem XIII. Expand
A Note on the Entscheidungsproblem
  • A. Church
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1936
It is shown that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent. Expand
The collected works
This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it hasExpand
On the Incompleteness Theorems
New proofs of both incompleteness theorems using quickly growing functions are given, without using the diagonalization lemma, and are tried to make the paper as model-theoretic as possible. Expand
Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems
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 inExpand
Die Vollständigkeit der Axiome des logischen Funktionenkalküls
Jakina da Whiteheadek eta Russellek logika eta matematika eraiki dutela ageriko zenbait proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikakoExpand