04208nam a22004575i 4500 978-0-387-36219-9 DE-He213 20260521091911.0 cr nn 008mamaa 100301s2006 xxu| s |||| 0|eng d 9780387362199 99780387362199 10.1007/0-387-36219-3 doi CICY 511.3 23 Komjáth, Péter. author. Problems and Theorems in Classical Set Theory [recurso electrónico] / by Péter Komjáth, Vilmos Totik. New York, NY : Springer New York, 2006. XII, 516 p. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Problem Books in Mathematics, 0941-3502 Problems -- Operations on sets -- Countability -- Equivalence -- Continuum -- Sets of reals and real functions -- Ordered sets -- Order types -- Ordinals -- Ordinal arithmetic -- Cardinals -- Partially ordered sets -- Transfinite enumeration -- Euclidean spaces -- Zorn's lemma -- Hamel bases -- The continuum hypothesis -- Ultrafilters on ? -- Families of sets -- The Banach-Tarski paradox -- Stationary sets in ?1 -- Stationary sets in larger cardinals -- Canonical functions -- Infinite graphs -- Partition relations -- ?-systems -- Set mappings -- Trees -- The measure problem -- Stationary sets in [?]<? -- The axiom of choice -- Well-founded sets and the axiom of foundation -- Solutions -- Operations on sets -- Countability -- Equivalence -- Continuum -- Sets of reals and real functions -- Ordered sets -- Order types -- Ordinals -- Ordinal arithmetic -- Cardinals -- Partially ordered sets -- Transfinite enumeration -- Euclidean spaces -- Zorn's lemma -- Hamel bases -- The continuum hypothesis -- Ultrafilters on ? -- Families of sets -- The Banach-Tarski paradox -- Stationary sets in ?1 -- Stationary sets in larger cardinals -- Canonical functions -- Infinite graphs -- Partition relations -- ?-systems -- Set mappings -- Trees -- The measure problem -- Stationary sets in [?]<? -- The axiom of choice -- Well-founded sets and the axiom of foundation. This is the first comprehensive collection of problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period between 1920-1970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis. The authors choose not to concentrate on the axiomatic framework, although some aspects are elaborated (axiom of foundation and the axiom of choice). Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. The problems are organized in a way that earlier problems help in the solution of later ones. For many problems, the authors trace the origin and provide proper references at the end of the solution. The book follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics. This is destined to become a classic, and will be an important resource for students and researchers. Péter Komjáth is a professor of mathematics at the Eötvös Lóránd University, Budapest. Vilmos Totik is a professor of mathematics at the University of South Florida, Tampa and University of Szeged. MATHEMATICS. COMBINATORICS. LOGIC, SYMBOLIC AND MATHEMATICAL. MATHEMATICS. MATHEMATICAL LOGIC AND FOUNDATIONS. COMBINATORICS. Totik, Vilmos. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780387302935 Problem Books in Mathematics, 0941-3502 http://dx.doi.org/10.1007/0-387-36219-3 Ver el texto completo en las instalaciones del CICY ddc ER 33422 33422 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 511.3 2025-07-10 08:39:56 2025-07-10 ER