[4] viXra:1411.0529 [pdf] submitted on 2014-11-21 07:00:54
Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, Ilanthenral K.
Comments: 242 Pages.
In this book the authors for the first time have ventured to study, analyse and investigate fuzzy and neutrosophic models and the experts opinion. To make such a study, innovative techniques and defined and developed. Several important conclusions about these models are derived using these new techniques. Open problems are suggested in this book.
Category: Set Theory and Logic
[3] viXra:1411.0528 [pdf] submitted on 2014-11-21 07:02:15
Authors: Vasantha Kandasamy, Florentin Smarandache, Ilanthenral K.
Comments: 275 Pages.
In this book the authors for the first time have merged vertices and edges of lattices to get a new structure which may or may not be a lattice but is always a graph. This merging is done for graph too which will be used in the merging of fuzzy models. Further merging of graphs leads to the merging of matrices; both these concepts play a vital role in merging the fuzzy and neutrosophic models.
Several open conjectures are suggested.
Category: Set Theory and Logic
[2] viXra:1411.0051 [pdf] submitted on 2014-11-07 05:57:21
Authors: Ricardo Alvira
Comments: 5 Pages.
It reviewes the difference between cocnepts involving Certainty/Uncertainty.
Category: Set Theory and Logic
[1] viXra:1411.0009 [pdf] submitted on 2014-11-01 23:51:59
Authors: Karan Doshi
Comments: 8 Pages.
Well-ordering of the Reals@@ presents a major challenge in Set theory. Under the standard Zermelo Fraenkel Set theory (ZF) with the Axiom of Choice (ZFC), a well-ordering of the Reals is indeed possible. However the Axiom of Choice (AC) had to be introduced to the original ZF theory which is then shown equivalent to the well-ordering theorem. Despite the result however, no way has still been found of actually constructing a well-ordered Set of Reals. In this paper the author attempts to generate a well ordered Set of Reals without using the AC i.e. under ZF theory itself using the Axiom of the Power Set as the guiding principle.
Category: Set Theory and Logic