Set Theory and Logic

   

Non-Archimedean Analysis on the Extended Hyperreal Line ∗R_d and the Solution of Some Very Old Transcendence Conjectures Over the Field Q.

Authors: Jaykov Foukzon

In 1980 F. Wattenberg constructed the Dedekind completion∗d of the Robinson non-archimedean field ∗ and established basic algebraic properties of ∗d [6]. In 1985 H. Gonshor established further fundamental properties of ∗d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion∗d in transcendental number theory were considered. We dealing using set theory ZFC  ∃(-model of ZFC).Given an class of analytic functions of one complex variable f ∈ z, we investigate the arithmetic nature of the values of fz at transcendental points en,n ∈ ℕ. Main results are: (i) the both numbers e   and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained.

Comments: 84 Pages.

Download: PDF

Submission history

[v1] 2015-06-18 15:52:27
[v2] 2015-07-08 13:53:53
[v3] 2015-07-19 07:43:00
[v4] 2015-11-28 01:02:00
[v5] 2016-02-08 00:58:31
[v6] 2016-02-19 13:37:03
[v7] 2016-03-05 13:46:48
[v8] 2016-04-30 08:12:21
[v9] 2016-05-14 14:11:23
[vA] 2017-02-15 03:38:49

Unique-IP document downloads: 89 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus