00000cmm a22000004a 4500 UP-99796217611212586 Buklod 20230215085534.0 m go j cr |n |||auu|a 110301s2011 xx u eng d 9783034800068 (eBook) 3034800061 (eBook) (iLib)UPD-00215704397 DML eng DMLUC QA 241 B85 2011eb Bukovsky, Lev. The structure of the real line [electronic resource] Lev Bukovsky. Basel Springer Basel 2011. 1 online resource (xiv, 536 p.) Monografie matematyczne 71. Preface -- 1 Introduction -- 2 The Real Line -- 3 Topology of Euclidean Spaces -- 4 Measure Theory -- 5 Useful Tools and Technologies -- 6 Descriptive Set Theory -- 7 Decline and Fall of the Duality -- 8 Special Sets of Reals -- 9 Additional Axioms -- 10 Undecidable Statements -- 11 Appendix -- Bibliography -- Index of Notation -- Index. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. The rapid development of set theory in the last fifty years, mainly in 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, descriptive set theory are revisited with the purpose to eliminate 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 it is shortly explained in the appendix. Each section contains a series of exercises with additional results. Electronic reproduction. New York SpringerLink c2011. Available via World Wide Web through SpringerLink. Numbers, Real. Set theory. Electronic books. Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-3-0348-0006-8 FO Monograph UPD DMLR Electronic Resource