The Relationship of Arithmetic As Two Twin Peano Arithmetic(s) and Set Theory: A New Glance From the Theory of Information

Metaphilosophy eJournal (Elseviers: SSRN) 12 (10):1-33 (2020)
  Copy   BIBTEX


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.



External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
What Is Quantum Information? Information Symmetry and Mechanical Motion.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-7.


Added to PP

419 (#49,443)

6 months
100 (#48,755)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Vasil Penchev
Bulgarian Academy of Sciences

Citations of this work

Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental Time.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (22):1-24.

Add more citations

References found in this work

A Mathematical Theory of Communication.Claude Elwood Shannon - 1948 - Bell System Technical Journal 27 (April 1924):379–423.
Was Sind und was Sollen Die Zahlen?Richard Dedekind - 1888 - Cambridge University Press.
Neuer Beweis für die Möglichkeit einer Wohlordnung.Ernst Zermelo - 1907 - Mathematische Annalen 65 (1):107-128.

Add more references