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The Foundations of Mathematics in the Theory of Sets.
・ISBN 978-0-521-17271-4 paper GB£ 69.00
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| 著者・編者 | Mayberry, John P., |
|---|---|
| シリーズ | Encyclopedia of Mathematics and its Applications |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2011 |
| ページ数 | 446 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-2202＞ |
解説
This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.