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The Relationship of Arithmetic as Two Twin Peano Arithmetic(s) and Set Theory: a New Glance from the Theory of Information

EasyChair Preprint no. 3911

33 pagesDate: July 20, 2020

Abstract

The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental mathematical problems of the present such as Fermat’s last theorem, four-color theorem as well as its new-formulated generalization as “four-letter theorem”, Poincaré’s conjecture, “P vs NP” are considered over again, from and within the new-founding conceptual reference frame of information, as illustrations. Simple or crucially simplifying solutions and proofs are demonstrated. The link between the consistent completeness of the system mathematics-physics on the ground of information and all the great mathematical problems of the present (rather than the enumerated ones) is suggested.

Keyphrases: consistent completeness of mathematics and physics unification of mathematics and physics, Hilbert arithmetic, nonstandard Peano arithmetic, Peano arithmetic, quantum information, two complimentary arithmetics

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@Booklet{EasyChair:3911,
  author = {Vasil Penchev},
  title = {The Relationship of Arithmetic as Two Twin Peano Arithmetic(s) and Set Theory: a New Glance from the Theory of Information},
  howpublished = {EasyChair Preprint no. 3911},

  year = {EasyChair, 2020}}
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