Journal of Advances in Mathematics and Computer Science

Set Theory INC# ∞# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper Inductive Definitions

Jaykov Foukzon *

Israel Institute of Technology, Haifa, Israel

*Author to whom correspondence should be addressed.

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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.

Keywords: Infinitary intuitionistic logic, nonstandard arithmetic, Goldbach and Euler theorem

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