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Naive Set Theory

por Paul R. Halmos

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340176,823 (4.02)4
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set­ theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.… (mais)
  1. 00
    Intermediate Set Theory por F. R. Drake (bertilak)
  2. 00
    Set Theory and Its Logic por W. V. Quine (billmcn)
    billmcn: Halmos takes sets as primitive objects instead of defining them in terms of logic as Quine does, which allows him to cover the same ground in less space at the cost of not having much to say about the Russell Paradox. Though dense, Halmos' book is short and accessible, and would be a good book to read before Quine as a way of scouting the territory.… (mais)
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This text shows its age -- it's heavily wordy and pretty light on presenting things in mathematical notation. Although I have never formally studied set theory, I didn't get much out of it, though it did serve to reinforce my knowledge of some of the algebra behind sets. ( )
  isovector | Dec 13, 2020 |
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Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set­ theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

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