Where academic tradition
meets the exciting future

Problem Solving by Being Strict on Finitism

Patrick Sibelius, Problem Solving by Being Strict on Finitism. TUCS Technical Reports 1168, TUCS, 2016.


The notorious tension between Godel's second incompleteness theorem of formal arithmetic and Gentzen's consistency theorem of formal arithmetic is approached in a strictly nitistic manner. A modi cation of the semantic tableau method is being used herein. Using it it is proved that formal Peano arithmetic is formally inconsistent with idea that Peano arithmetic is true in the standard First-order model of arithmetic. Commonly accepted ways to evade such a result are commented on. By considering a strictly nitistic version (interpretation) of the proof of Cantor's Theorem about the cardinality of the set of real numbers an argument is presented that entails that P =/= NP.


Full publication in PDF-format

BibTeX entry:

  title = {Problem Solving by Being Strict on Finitism},
  author = {Sibelius, Patrick},
  number = {1168},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2016},
  keywords = {Godel's second incompleteness theorem, Gentzen's consistency theorem, Hilbert's Thesis, Church-Turing Thesis, First-order logic, Peano arithmetic, the standard First-order structure of arithmetic, discrete linear orders, semantic tableau method, Skolem function symbols, Cantor's theorem, P versus NP problem},
  ISBN = {978-952-12-3467-5},

Belongs to TUCS Research Unit(s): Other

Edit publication