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Set Theory INC# ∞# Based on Innitary Intuitionistic Logic with Restricted Modus Ponens Rule. Hyper Inductive Denitions. Application in Transcendental Number Theory. Generalized Lindemann-Weierstrass Theorem

Jaykov Foukzon

Journal of Advances in Mathematics and Computer Science · pp. 70–119 · Published 8 Oct 2021

10.9734/jamcs/2021/v36i830394

Abstract

In this paper intuitionistic set theory INC#∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained without any references to Catalan conjecture. Main results are: (i) number ee is transcendental; (ii) the both numbers e + π and e − π are irrational.

Innitary intuitionistic logic nonstandard arithmetic Goldbach and Euler theorem nonstandard analisys Lindemann-Weierstrass theorem

References (12)

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  5. 5 NONSTANDARD METHODS IN STOCHASTIC ANALYSIS AND MATHEMATICAL PHYSICS [DOI]
  6. 6 Infinite terms and a system of natural deduction
  7. 7 Set Theory INC# Based on Intuitionistic Logic with Restricted Modus Ponens Rule (Part. I) [DOI]
  8. 8 Catalan’s Conjecture: Another old Diophantine problem solved [DOI]
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Cited by 10

Internal Set Theory IST# Based on Hyper Infinitary Logic with Restricted Modus Ponens Rule: Nonconservative Extension of the Model Theoretical NSA

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The Solution of the Invariant Subspace Problem in Complex Hilbert Space: External non-Archimedean field *Rc by Cauchy Completion of the internal Non-Archimedean field *R (Part I)

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The Solution of the Invariant Subspace Problem. Complex Hilbert Space. External Countable Dimensional Linear spaces Over Field \(^*\mathbb{R}_c^\#\). Part II.

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Internal Set Theory IST <sup>#</sup>Based on Gyper Infinitary Logic With Restricted Modus Ponens Rule

Jaykov Foukzon · SSRN Electronic Journal · 2022

Set Theory NC_{∞}^{} Based on Bivalent Infinitary Logic with Restricted Modus Ponens Rule.Basic Real Analysis on External Non-Archimedean Field ℝ_{c}^{}. Basic Complecs Analysis on External Field ℂ_{c}^{}=ℝ_{c}^{}[i].

Jaykov Foukzon · SSRN Electronic Journal · 2021

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