What do you think?
Rate this book
Sets Logic and Axiomatic Theories Edition
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 of 1 review
January 16, 2016
After reading the Penrose book (The Road to Reality), I'm beginning to review my math in the hopes of going a little bit beyond where I stopped in college. I began by re-reading this little book on the foundations. It's actually an abridged edition of the first chapters of the author's Set Theory and Logic.
The book is in four chapters; the first chapter is an intuitive introduction to set theory, the second chapter is on logic (statement logic and first order predicate logic), the third chapter is on axiomatic theories and develops the material of the first two chapters in a more rigorous way, and the fourth chapter is an introduction to Boolean algebras.
According to the preface, the book is intended for four groups: undergraduates who are planning to take a course in abstract algebra, future and present high school math teachers, and "brilliant" high school students. He says that the first two and a half chapters constitute about what "every educated person" should know about the foundations of math. I think his assumptions about high school students and "educated" people may be outdated, at least in the U.S. today after almost a half century of dumbed-down math -- this book was written in 1961, when math teaching was becoming more rigorous rather than less -- but for the most part it is a very simple introduction given how comprehensive it is. Some reviews I have seen have said that you already have to understand the material to understand the book, but I think that is only true of the very end of the last chapter, where he covers homomorphism and ideals in a very condensed section which is rather hard to understand without some background in group theory.
The book is in four chapters; the first chapter is an intuitive introduction to set theory, the second chapter is on logic (statement logic and first order predicate logic), the third chapter is on axiomatic theories and develops the material of the first two chapters in a more rigorous way, and the fourth chapter is an introduction to Boolean algebras.
According to the preface, the book is intended for four groups: undergraduates who are planning to take a course in abstract algebra, future and present high school math teachers, and "brilliant" high school students. He says that the first two and a half chapters constitute about what "every educated person" should know about the foundations of math. I think his assumptions about high school students and "educated" people may be outdated, at least in the U.S. today after almost a half century of dumbed-down math -- this book was written in 1961, when math teaching was becoming more rigorous rather than less -- but for the most part it is a very simple introduction given how comprehensive it is. Some reviews I have seen have said that you already have to understand the material to understand the book, but I think that is only true of the very end of the last chapter, where he covers homomorphism and ideals in a very condensed section which is rather hard to understand without some background in group theory.
Displaying 1 of 1 review