Corpus ID: 25401348

Gödel for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) Gödel's First Incompleteness Theorem

  title={G{\"o}del for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) G{\"o}del's First Incompleteness Theorem},
  author={Dan Gusfield},
  journal={arXiv: Logic},
  • D. Gusfield
  • Published 20 September 2014
  • Mathematics, Computer Science
  • arXiv: Logic
Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to riddles and paradoxes, but do not attempt to present rigorous, complete proofs; or they do present rigorous proofs, but in the traditional style of mathematical logic, with all of its heavy notation and difficult definitions, and technical issues which… Expand
2 Citations
A dual identity based symbolic understanding of the Godel's incompleteness theorems, P-NP problem, Zeno's paradox and Continuum Hypothesis
A semantic analysis of formal systems is undertaken, wherein the duality of their symbolic definition based on the "State of Doing" and "State of Being" is brought out. We demonstrate that when theseExpand
The "cardinality of extended solution set" criterion for establishing the intractability of NP problems
  • U. Arun
  • Mathematics, Computer Science
  • ArXiv
  • 2020
A criterion termed as "cardinality of extended solution set" is conceived to ascertain the (non)randomness of any sequence and can be used to establish the (in)tractability of any problem depending on whether its solutions are random or non-random. Expand