# Set Theory and Logic

## 1607 Submissions

[3] **viXra:1607.0421 [pdf]**
*replaced on 2016-12-07 08:10:32*

### The Theory of Ultralogics, the Modified Robinson Approach, and GID

**Authors:** Robert A. Herrmann

**Comments:** 8 Pages.

The basic mathematical aspects of the GGU and GID models are discussed. As an illustration, the modified Robinson approach is used to give a more direct prediction as to the composition of ultra-propertons. Relative to logic-systems, the refined developmental paradigm is applied to the General Intelligent Design (GID) model and the basic GID statements are given.

**Category:** Set Theory and Logic

[2] **viXra:1607.0153 [pdf]**
*submitted on 2016-07-13 04:47:18*

### A Phenomenon in Gödel’s Incompleteness Theorems

**Authors:** S.Kalimuthu

**Comments:** 06 Pages. NA

According to James R. Meyer, In mathematics, a theorem is intended to be a term for a very precise and definite concept - a theorem is a statement that is proved, using rigorous mathematical reasoning, to follow according to a set of logical rules, from a set of initial statements. These initial statements are usually called axioms, and these are statements that are accepted without being proven. The set of logical rules which determine how one statement can follow from another are usually called the rules of inference . And basically, Gödel's incompleteness theorem is any statement that says that for every formal mathematical system, there are sentences that cannot be proved to be true or false in that system.

**Category:** Set Theory and Logic

[1] **viXra:1607.0124 [pdf]**
*submitted on 2016-07-11 02:37:20*

### Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset

**Authors:** Florentin Smarandache

**Comments:** 170 Pages.

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities.
He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}.
This is no surprise with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components.

**Category:** Set Theory and Logic