[5] **viXra:1710.0309 [pdf]**
*submitted on 2017-10-28 12:24:53*

**Authors:** George Cherevichenko

**Comments:** 15 Pages.

Using explicit weakenings, we can define alpha-conversion by simple equations without any mention of free variables.

**Category:** Set Theory and Logic

[4] **viXra:1710.0237 [pdf]**
*submitted on 2017-10-21 10:32:06*

**Authors:** Anders Lindman

**Comments:** 3 Pages.

The fundamental set theory (FST) is defined as an axiomatic set theory using nonclassical three-valued logic in the foundation and classical two-valued logic in its applications. In this way the nonclassical logic becomes encapsulated and is only used for resolving inconsistencies such as Russell's paradox.

**Category:** Set Theory and Logic

[3] **viXra:1710.0226 [pdf]**
*submitted on 2017-10-20 08:20:23*

**Authors:** Divyendu Priyadarshi

**Comments:** 2 Pages.

I have argued that the Real Numbers do not form a set in the sense that they lack any specific character to define them. I am not a professional mathematician but a Physics teacher. So my arguments may lack mathematical precision. All suggestions and criticisms are heartily welcome.

**Category:** Set Theory and Logic

[2] **viXra:1710.0223 [pdf]**
*submitted on 2017-10-19 23:09:13*

**Authors:** Anders Lindman

**Comments:** 3 Pages.

The set of standard numbers D is constructed from an axiom of infinite fraction sum together with the power set of the set of all rational numbers in the form 2^-n. The power set contains all possible infinite binary sequences who represent the fraction part of the standard numbers together with the integers for the whole number part. The set of standard numbers includes the rational numbers and forms a field (D, +, *) similar to, yet distinct from the set of real numbers R.

**Category:** Set Theory and Logic

[1] **viXra:1710.0035 [pdf]**
*submitted on 2017-10-04 01:50:21*

**Authors:** Dmitri Martila

**Comments:** 4 Pages.

Derived the Statistics of the un-solved problems (conjectures). The probability, what a conjecture will be solved is 50 %. The probability, that a conjecture is true is p=37 %. The probability, what we get to know the latter is psi=29 %....

**Category:** Set Theory and Logic