# Set Theory and Logic

## 1108 Submissions

[2] **viXra:1108.0025 [pdf]**
*submitted on 19 Aug 2011*

### Logical Ramblings

**Authors:** Thomas Evans

**Comments:** 11 pages

I present extensions to logic theory whose utilitarian application contains itself
in the form of a developmental, logical framework determinant of all being, and then
derive several applications thereof to areas of general quantum theory and pure
mathematics, providing solutions to 2 longstanding relevant problems: P vs NP and the
Riemann Hypothesis.

**Category:** Set Theory and Logic

[1] **viXra:1108.0011 [pdf]**
*submitted on 4 Aug 2011*

### Neutrosophic Logics on Non-Archimedean Structures

**Authors:** Andrew Schumann

**Comments:** 23 pages

We present a general way that allows to construct systematically analytic
calculi for a large family of non-Archimedean many-valued logics:
hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized
by a special format of semantics with an appropriate rejection
of Archimedes' axiom. These logics are built as different extensions of
standard many-valued logics (namely, Lukasiewicz's, Gödel's, Product,
and Post's logics). The informal sense of Archimedes' axiom is that anything
can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is innite and
it is not well-founded and well-ordered. We consider two cases of
non-Archimedean multi-valued logics: the rst with many-validity in the interval
[0; 1] of hypernumbers and the second with many-validity in the
ring Zp of p-adic integers. On the base of non-Archimedean valued logics,
we construct non-Archimedean valued interval neutrosophic logics by
which we can describe neutrality phenomena.

**Category:** Set Theory and Logic