Set Theory 1

This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advance……続きを見る

Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It c……続きを見る

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite order……続きを見る

Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math……続きを見る

At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate……続きを見る

The System of the World by Isaac Newton. Sir Isaac Newton (1642–1727) was an English physicist and mathematician who is widely recognised as one of the most influential scientists of all time and as……続きを見る

Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polyto……続きを見る

The Language of Symmetry is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. It expl……続きを見る

The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ……続きを見る

Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of fixed-point theory and its applications with a strong focus on examples, p……続きを見る

The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after it……続きを見る

Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concis……続きを見る

This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about t……続きを見る

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly……続きを見る

The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem ……続きを見る

This volume takes its name from a popular series of intensive mathematics workshops hosted at institutions in Appalachia and surrounding areas. At these meetings, internationally prominent set theor……続きを見る

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most imp……続きを見る

This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. ……続きを見る

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. Th……続きを見る

"A gripping guide to the modern taming of the infinite."ーThe New York Times. With a new introduction by Neal Stephenson. Is infinity a valid mathematical property or a meaningless abstraction? Davi……続きを見る

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mat……続きを見る

Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does ……続きを見る

This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algeb……続きを見る

Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets whi……続きを見る

Psychic abilities are innate to all humans. This illustrated book helps you to explore and develop this inner part of yourself through a series of meditations and exercises. Through these you will l……続きを見る

This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set……続きを見る

Relation theory originates with Hausdorff (Mengenlehre 1914) and Sierpinski (Nombres transfinis, 1928) with the study of order types, specially among chains = total orders = linear orders. One of it……続きを見る

This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the ……続きを見る

This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters……続きを見る

This volume provides a forum which highlights new achievements and overviews of recent developments of the thriving logic groups in the Asia-Pacific region. It contains papers by leading logicians a……続きを見る