Set Theory: An Introduction 2nd Edition by Robert L. Vaught (PDF)

Description

By its nature, set theory does not depend on any previous mathematical knowl­ edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub­ ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann’s proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann’s ‘inner model’ proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.

User’s Reviews

Editorial Reviews: Review “One of [the book’s] strengths is the author’s voice. His prose is clear and correct…The text is quite concise.”–Mathematical Reviews”The volume is in a clear and interesting style and is highly recommended to undergraduate students of mathematics as well as philosophy.” –Acta Sci. Math. (on the first edition)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This skinny little paperback is supposedly aimed at undergraduate math students looking for their first experience with rigorous set theory. Unfortunately, the book doesn’t do a good job of addressing the needs of such an audience.Instead, the book seems more like a set of instructor’s notes for someone *teaching* such a course. The book assumes far too much background knowledge for an introductory text, and its explanations are often just sketches that need to be fleshed out by a skilled instructor.Another problem with this book is its incomplete bibliography. Rather than include full references, the author just supplies a last name and a date, and refers the reader to the bibliography of some other book — where the complete reference can be found. Unfortunately, some of these meta-sources are long out of print, so there’s no way to follow the reference. Very poor.There are much better books out there covering the same territory: Enderton is the standard; the introductory text by Hrbacek and Jech is another.

⭐Short and sweet.

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