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 *
Israel Institute of Technology, Haifa, Israel.
*Author to whom correspondence should be addressed.
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.
Keywords: Innitary intuitionistic logic, nonstandard arithmetic, Goldbach and Euler theorem, nonstandard analisys, Lindemann-Weierstrass theorem