Open AccessSet Theory INC# ∞# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper Inductive Definitions
Author(s) -
Jaykov Foukzon
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i430359
Subject(s) - modus ponens , goldbach's conjecture , mathematics , set (abstract data type) , conjecture , mathematical induction , number theory , discrete mathematics , algebra over a field , rule of inference , pure mathematics , calculus (dental) , computer science , artificial intelligence , inference , programming language , medicine , geometry , dentistry
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 anyreferences to Catalan conjecture.