Set Theory
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Recent papers in Set Theory
A translation of the π-calculus into the MONSTR graph rewriting language is described and proved correct. The translation illustrates the heavy cost in practice of faithfully implementing the communication primitive of the π-calculus and... more
Traditional agenda-setting theory is about the influence of mass media on the public's focus of attention, who and what people are thinking about. The expanded theory of agenda setting tested here during the 1995 regional and... more
Is attention both necessary and sufficient for consciousness? Call this central question of this treatise, “Q.” We commonly have the experience of consciously paying attention to something, but is it possible to be conscious of something... more
Online material for a Z course based on the book by the author. This includes slides for some chapters and the exercises. Updated in July 1998 with minor corrections and improved formatting.
The Continuum Problem has inspired set theorists and philosophers since the days of Cantorian set theory. In the last 15 years, W. Hugh Woodin, a leading set theorist, has not only taken it upon himself to engage in this question, he has... more
A \emph{standard formalization} of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $\in$). Patrick Suppes (\cite{sup92}) expressed... more
The systematic implications of irrational numbers, for those interested.
The attitude to use whole numbers to point out notes in the twelve-tone chromatic scale dates back to about a century ago. Although the trend to quantify and to catalogue has always been present in Western music, it was with the... more
RESUMEN La demostracion habitual del Segundo Teorema de Incompletud de Godel a partir de teorias debiles como IΣ1 es larga y tecnicamente intrincada. Raramente se dan todos los detalles y en muchos casos se omiten completamente apelando a... more
In the framework of the philosophy of contemporary mathematics, Hellman and Awodey both hold an interesting discussion on the role of Zermelo-Fraenkel Set Theory and Category Theory in the perspective of a good foundation for mathematics.... more
Indicates that everything standing on top of naive set theory is also proven.
It is generally agreed that faces are not recognized only by utilizing some holistic search among all learned faces, but also through a feature analysis that aimed to specify more important features of each specific face. This paper... more
A software model is a widely used technique to specify software. A UML model may contain different diagrams and a diagram is built from different elements. Each element is restraint to certain constraint or well-formedness rules (WFR).... more
The emergence of big data analytics as a way of deriving insights from data brought excitement to mathematicians, statisticians, computer scientists and other professionals. However, the absence of a mathematical foundation for analytics... more
1981. A note on categoricity and completeness, History and Philosophy of Logic 2, 113–19. Current study of axiomatic method presupposes concepts and results of string theory and set theory. But axiomatic method was vigorously pursued in... more
As exposed in this paper, Cantor's diagonal argument seems to lead to a serious paradox.
One of the most popular methods to visualize the overlap and differences between data sets is the Venn diagram. Venn diagrams are especially useful when they are ‘area-proportional’ i.e. the sizes of the circles and the overlaps... more
What shapes peace, and how can peace be successfully built in those countries affected by armed conflict? This paper examines peacebuilding in the aftermath of civil wars in order to identify the conditions for post-conflict peace. The... more
The notion of a topological Ramsey space was introduced by Carlson some 30 years ago. Studying the topological Ramsey space of variable words, Carlson was able to derive many classical combinatorial results in a unifying manner.
This paper aims to illuminate the fundamental flaws of the basic theory of arithmetic. No further introduction needed.
In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the 'thinking... more
Lip reading has wide spread application, e.g. audiovisual Automatic Speech Recognition (A V-ASR), silent speech interface and person identification. Lip segmentation is one of important step in lip reading, because it provides basic... more
This chapter is devoted to introducing the theories of interval algebra to people who are interested in applying the interval methods to uncertainty analysis in science and engineering. In view of this purpose, we shall introduce the key... more
Resumen. Los procesos cognitivos involucrados en la conceptualización, la categorización, y sus implicaciones para áreas como la lingüística y la lógica, son un tema recurrente en la filosofía contemporánea de la mente y del lenguaje,... more
Alex Ling seizes upon the philosophy of Alain Badiou to clarify a central question in film scholarship: ‘can cinema be thought?’ Treating this question on three levels, the author first asks if we can really think what cinema is, at an... more