This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal…
Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretic…
"This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and s…
The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathe…
by Joyal, André, Moerdijk, Ieke
fromLondon Mathematical Society lecture note series
This book offers a new, algebraic, approach to set theory.
"Preface To the student: We think that the theory dealing with what is hard about computation (and what is impossible!) is challenging but fun. This book grows out of these ideas, and our approach to teaching a course in computational complexity. There is no doubt that some of t…
"Preface To the student: We think that the theory dealing with what is hard about computation (and what is impossible!) is challenging but fun. This book grows out of these ideas, and our approach to teaching a course in computational complexity. There is no doubt that some of t…
Annotation
The best introductory text we have seen.? Cosmos. Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set …
Biographical note: Professor Martin Zeman, Institut für formale Logik, University Vienna, Vienna, Austria. Main description: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardina…
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the s…
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the s…
The core model, K, is a generalization of Gödel's constructible universe of set theory; K is used to produce 'fine structural' results of a less restrictive kind. This book aims to introduce the core model to those with a basic knowledge of axiomatic set theory. The covering lem…
This volume presents a novel approach to set theory that is entirely operational. This approach avoids the existential axioms associated with traditional Zermelo-Fraenkel set theory, and provides both a foundation for set theory and a practical approach to learning the subject. …
"Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and th…
Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form …
This textbook gives students a comprehensive introduction to formal methods and their application in software and hardware specification and verification. It has three parts: The first part introduces some fundamentals in formal methods, including set theory, functions, finite s…
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff{u2019}s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way th…
