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Set Theory with a Universal Set - T. E. Forster - Bog - Oxford University Press - Plusbog.dk

Set Theory with a Universal Set - T. E. Forster - Bog - Oxford University Press - Plusbog.dk

Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by other sets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science.The second edition still concentrates largely on Quine''s New Foundations, reflecting the author''s belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the set theories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.

DKK 827.00
1

Monogatari Series Box Set, Final Season - Nisioisin - Bog - Vertical, Inc. - Plusbog.dk

Monogatari Series Box Set, Final Season - Nisioisin - Bog - Vertical, Inc. - Plusbog.dk

From the popular MONOGATARI Series by NisiOisiN comes the final season of the novels in a beautiful new box set. VOFAN, who has created beautiful cover artwork since the beginning of the series, has created exclusive new artwork just for this project. This box set will feature the new artwork and complete the MONOGATARI box set collection. Plus a beautiful art card included as a bonus item, which showcases the box set artwork.

DKK 861.00
1

Hesitant Fuzzy Set - Bahram Farhadinia - Bog - Springer Verlag, Singapore - Plusbog.dk

Hesitant Fuzzy Set - Bahram Farhadinia - Bog - Springer Verlag, Singapore - Plusbog.dk

Covering a wide range of notions concerning hesitant fuzzy set and its extensions, this book provides a comprehensive reference to the topic. In the case where different sources of vagueness appear simultaneously, the concept of fuzzy set is not able to properly model the uncertainty, imprecise and vague information. In order to overcome such a limitation, different types of fuzzy extension have been introduced so far. Among them, hesitant fuzzy set was first introduced in 2010, and the existing extensions of hesitant fuzzy set have been encountering an increasing interest and attracting more and more attentions up to now. It is not an exaggeration to say that the recent decade has seen the blossoming of a larger set of techniques and theoretical outcomes for hesitant fuzzy set together with its extensions as well as applications. As the research has moved beyond its infancy, and now it is entering a maturing phase with increased numbers and types of extensions, this book aims to give a comprehensive review of such researches. Presenting the review of many and important types of hesitant fuzzy extensions, and including references to a large number of related publications, this book will serve as a useful reference book for researchers in this field.

DKK 986.00
1

A Logical Foundation for Potentialist Set Theory - Sharon Berry - Bog - Cambridge University Press - Plusbog.dk

A Logical Foundation for Potentialist Set Theory - Sharon Berry - Bog - Cambridge University Press - Plusbog.dk

In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.

DKK 773.00
1

Classic Set Theory - D. C. Goldrei - Bog - Taylor & Francis Ltd - Plusbog.dk

Classic Set Theory - D. C. Goldrei - Bog - Taylor & Francis Ltd - Plusbog.dk

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers Defining natural numbers in terms of sets The potential paradoxes in set theory The Zermelo-Fraenkel axioms for set theory The axiom of choice The arithmetic of ordered sets Cantor''s two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these. The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed. Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

DKK 819.00
1

Intuitive Axiomatic Set Theory - Jose L Garcia - Bog - Taylor & Francis Ltd - Plusbog.dk

Intuitive Axiomatic Set Theory - Jose L Garcia - Bog - Taylor & Francis Ltd - Plusbog.dk

Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.

DKK 825.00
1