Notes on Set Theory / by Yiannis Moschovakis
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 1994. |
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1994 |
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| 書誌ID | OB01019518 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 1. Introduction -- 2. Equinumerosity -- 3. Paradoxes and axioms -- 4. Are sets all there is? -- 5. The natural numbers -- 6. Fixed points -- 7. Well ordered sets -- 8. Choices -- 9. Choice's consequences -- 10. Baire space -- 11. Replacement and other axioms -- 12. Ordinal numbers -- A. The real numbers -- Congruences -- Fields -- Ordered fields -- Uniqueness of the rationals -- Existence of the rationals -- Countable, dense, linear orderings -- The archimedean property -- Nested interval property -- Dedekind cuts -- Existence of the real numbers -- Uniqueness of the real numbers -- Problems for Appendix A -- B. Axioms and universes -- Set universes -- Propositions and relativizations -- Rieger universes -- Rieger's Theorem -- Bisimulations -- The antifounded universe -- Aczel's Theorem -- Problems for Appendix B. License restrictions may limit access Summary: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning |
| 著者標目 | *Moschovakis, Yiannis SpringerLink (Online service) |
| 統一書名標目 | Undergraduate Texts in Mathematics, |
| 件 名 | LCSH:Mathematical logic FREE:Mathematical Logic and Foundations |
| 分 類 | LCC:QA8.9-10.3 DC23:511.3 |
| 巻冊次 | ISBN:9781475741537 RefWorks出力（各巻） print ; ISBN:9781475741551 RefWorks出力（各巻） print ; ISBN:9781475741544 RefWorks出力（各巻） print ; ISBN:9780387941806 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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