[5] **viXra:1508.0309 [pdf]**
*submitted on 2015-08-30 19:26:33*

**Authors:** Minseong Kim

**Comments:** 2 Pages.

In computer science, a character set $\Sigma$ is often defined. Then, Kleene plus and Kleene star for formal language are defined. Then, $\Sigma^{+} = \Sigma^{*}\Sigma$ is proved, which means every string (set) in $\Sigma^{+}$ can be represented as a concatenation of a set in $\Sigma^{*}$ and a set in $\Sigma$. However, if one forms a set that cannot be defined by a formula but what people would believe as existing, then while the proof itself does not break down, it may be possible that state of matter is inconsistent. This paper explores this possibility.

**Category:** Set Theory and Logic

[4] **viXra:1508.0299 [pdf]**
*submitted on 2015-08-29 08:36:40*

**Authors:** Samuel Amok

**Comments:** 1 Page.

In this paper, I answer to a question that has been raised in http://www.les-mathematiques.net/phorum/read.php?16,1137927,1137947#msg-1137947

**Category:** Set Theory and Logic

[3] **viXra:1508.0284 [pdf]**
*submitted on 2015-08-27 01:08:39*

**Authors:** Shawkat Alkhazaleh, Emad Marei

**Comments:** 112 Pages.

In 1995 Smarandache introduced the concept of
neutrosophic set which is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. In 2013 Maji introduced the concept of neutrosophic soft
set theory as a general mathematical tool for dealing with uncertainty.

**Category:** Set Theory and Logic

[2] **viXra:1508.0161 [pdf]**
*submitted on 2015-08-20 09:19:58*

**Authors:** Alex Patterson

**Comments:** 12 Pages. Special thanks to Michael J. Burns

This paper uses its own peculiar lettering system for each paragraph.
This paper proposes an overall solution to Godel’s incompleteness theorem and the Gödel sentence. Both are handled as one, by using Gödel numbers as the exemplary objects of incompleteness.
New terms and tools are introduced for quantification that creates a more synthetic (logical, reasonable, coherent) intervention and inter-weaving into these now classical problems of the assumptions in the Gödel material and literature.
Asymptotes are used within vertical and horizontal graphs to justify a future that need not be seen as a future in the sense of grammatical future-tense, but as a potential part such systems themselves that we deal with respect to incompleteness.
The thesis is that we can approach incompleteness by using theoretical reasoning and available tools that are allowed in theoretical reasoning to critique the very theory of incompleteness itself. That is the essential Abstract Thesis. It will be seen that a real attempt is attempted.

**Category:** Set Theory and Logic

[1] **viXra:1508.0089 [pdf]**
*replaced on 2016-02-13 08:42:50*

**Authors:** Peiman Ghasemi

**Comments:** 7 Pages.

Until the current moment, mankind is not realized that there is a diverse population of intelligent civilizations living in our universe. In the current article we will deduce the occurrence/existence of extraterrestrial life by mathematical proof. I would show you that even inside our galaxy, the Milky Way, a sufficient number of alien creatures are living. The first section includes an algebraic probabilistic proof when the event of life is not highly biased and the second section includes a proof by contradiction that describes the event fundamentally. It's a mathematical proof for the extraterrestrial life debate, for the first time in mankind's history.

**Category:** Set Theory and Logic