# Set Theory and Logic

## 1310 Submissions

[3] **viXra:1310.0221 [pdf]**
*submitted on 2013-10-24 16:37:16*

### The Characteristic Function of a Neutrosophic Set

**Authors:** A. A. Salama, Mohamed eisa, Florentin Smarandache

**Comments:** 1 Page.

The purpose of this paper is to introduce and study the characteristic
function of a neutrosophic set. After given the fundamental definitions of
neutrosophic set operations generated by, we obtain several properties, and discussed
the relationship between neutrosophic sets generated by Ng and others. Finally, we
introduce the neutrosophic topological spaces generated by Ng . Possible application
to GIS topology rules are touched upon.

**Category:** Set Theory and Logic

[2] **viXra:1310.0075 [pdf]**
*replaced on 2014-04-18 11:11:16*

### The Continuum Hypothesis

**Authors:** Daniel Cordero Grau

**Comments:** 3 Pages.

In this paper we prove the continuum hypothesis by categorical logic, proving that the theory of initial ordinals and the theory of cardinals are isomorphic. To prove that the theorems of the theory of cardinals are theorems of the theory of initial ordinals, and conversely, the theorems of the theory of initial ordinals are theorems of the theory of cardinals, and so, since isomorphic structures are isomorphic theories by the fundamental theorem of mathematical logic, cardinals and initial ordinals are isomorphic structures, we use the definition of a theory, the definition of an isomorphism of structures in its equivalent form, the definition of an isomorphism of categories, the definition of a structure, the definition of a formal language, the definition of a functor, the definition of a category, the axioms of mathematical logic and the axioms of the theory of categories, which include the Gödel-Bernays-von Neumann axioms, so as to apply both the theorem on the comparablity of ordinals to the theory of cardinals and the fundamental theorem of cardinal arithmetic to the theory of ordinals.

**Category:** Set Theory and Logic

[1] **viXra:1310.0006 [pdf]**
*replaced on 2016-03-12 20:09:52*

### The Intractability Computational Complexity Class

**Authors:** Daniel Cordero Grau

**Comments:** 2 Pages.

In this paper we prove the Space Time Computational Intractability, the Fundamental Theorem of Computational Complexity, proving the Quantum Computation Intractability

**Category:** Set Theory and Logic