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
2021 ◽
pp. 70-119
Keyword(s):
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.
2021 ◽
pp. 90-112
2008 ◽
Vol 73
(4)
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pp. 1315-1327
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2015 ◽
pp. 297-306
2003 ◽
Vol 9
(6)
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pp. 1401-1409
2007 ◽
Vol 48
(4)
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pp. 473-488
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