Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician
Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician

Author: Winfried Just

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 240

ISBN-13: 0821805282

DOWNLOAD EBOOK

This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.

Discovering Modern Set Theory. I: The Basics
Discovering Modern Set Theory. I: The Basics

Author: Winfried Just

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 230

ISBN-13: 0821802666

DOWNLOAD EBOOK

This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

Discovering Modern Set Theory
Discovering Modern Set Theory

Author: Winfried Just

Publisher: American Mathematical Society(RI)

Published: 1996

Total Pages: 230

ISBN-13: 9781470420680

DOWNLOAD EBOOK

This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

Introduction to Modern Set Theory
Introduction to Modern Set Theory

Author: Judith Roitman

Publisher: John Wiley & Sons

Published: 1990-01-16

Total Pages: 188

ISBN-13: 9780471635192

DOWNLOAD EBOOK

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

Fundamentals of Mathematical Logic
Fundamentals of Mathematical Logic

Author: Peter G. Hinman

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 698

ISBN-13: 1351991752

DOWNLOAD EBOOK

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Basic Set Theory
Basic Set Theory

Author: Nikolai Konstantinovich Vereshchagin

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 130

ISBN-13: 0821827316

DOWNLOAD EBOOK

The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.