| The Structure of the Real Line 2011 Edition Contributor(s): Bukovský, Lev (Author) |
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ISBN: 3034803214 ISBN-13: 9783034803212 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: April 2013 |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory - Mathematics | Topology - General - Mathematics | Mathematical Analysis |
| Dewey: 511.322 |
| Series: Monografie Matematyczne |
| Physical Information: 1.3" H x 6.1" W x 9" (1.70 lbs) 542 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results. |