000			04161nam a22002057a 4500
003			CUTN
005			20250124121250.0
008			250124b |||||||| |||| 00| 0 eng d
020			_a9781071603710
041			_aEnglish
082			_a511.322 _bKOM
100			_aKomjáth, Peter
245			_aProblems and Theorems in Classical Set Theory /
260			_bSpringer, _c2006.
300			_a516p.: _bill.;
505			_tFront Matter Pages 1-1 Operations on sets Pages 3-7 Countability Pages 9-12 Equivalence Pages 13-14 Continuum Pages 15-18 Sets of reals and real functions Pages 19-21 Ordered sets Pages 23-31 Order types Pages 33-36 Ordinals Pages 37-41 Ordinal arithmetic Pages 43-50 Cardinals Pages 51-54 Partially ordered sets Pages 55-57 Transfinite enumeration Pages 59-61 Euclidean spaces Pages 63-64 Zorn’s lemma Pages 65-66 Hamel bases Pages 67-69 The continuum hypothesis Pages 71-73 Ultrafilters on ω Pages 75-78 Families of sets Pages 79-80 The Banach-Tarski paradox Pages 81-83 Stationary sets in ω1 Pages 85-87 Stationary sets in larger cardinals Pages 89-92 Canonical functions Pages 93-94 Infinite graphs Pages 95-99 Partition relations Pages 101-105 Δ-systems Pages 107-108 Set mappings Pages 109-110 Trees Pages 111-115 The measure problem Pages 117-121 Stationary sets in [λ]<κ Pages 123-125 The axiom of choice Pages 127-128 Well-founded sets and the axiom of foundation Pages 129-132 Solutions Front Matter Pages 133-133 Operations on sets Pages 135-146 Countability Pages 147-157 Equivalence Pages 159-162 Continuum Pages 163-172 Sets of reals and real functions Pages 173-183 Ordered sets Pages 185-212 Order types Pages 213-222 Ordinals Pages 223-235 Ordinal arithmetic Pages 237-263 Cardinals Pages 265-273 Partially ordered sets Pages 275-284 Transfinite enumeration Pages 285-297 Euclidean spaces Pages 299-307 Zorn’s lemma Pages 309-316 Hamel bases Pages 317-326 The continuum hypothesis Pages 327-339 Ultrafilters on ω Pages 341-349 Families of sets Pages 351-357 The Banach-Tarski paradox Pages 359-368 Stationary sets in ω1 Pages 369-376 Stationary sets in larger cardinals Pages 377-383 Canonical functions Pages 385-387 Infinite graphs Pages 389-403 Partition relations Pages 405-420 Δ-systems Pages 421-425 Set mappings Pages 427-432 Trees Pages 433-451 The measure problem Pages 453-462 Stationary sets in [λ]<κ Pages 463-470 The axiom of choice Pages 471-479 Well-founded sets and the axiom of foundation Pages 481-489 Back Matter Pages 491-516
520			_aAlthough the ?rst decades of the 20th century saw some strong debates on set theory and the foundation of mathematics, afterwards set theory has turned into a solid branch of mathematics, indeed, so solid, that it serves as the foundation of the whole building of mathematics. Later generations, honest to Hilbert’s dictum, “No one can chase us out of the paradise that Cantor has created for us” proved countless deep and interesting theorems and also applied the methods of set theory to various problems in algebra, topology, in?nitary combinatorics, and real analysis. The invention of forcing produced a powerful, technically sophisticated tool for solving unsolvable problems. Still, most results of the pre-Cohen era can be digested with just the knowledge of a commonsense introduction to the topic. And it is a worthy e?ort, here we refer not just to usefulness, but, ?rst and foremost, to mathematical beauty. In this volume we o?er a collection of various 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 fromtheperiod,say,1920–1970.Manyproblemsarealsorelatedtoother?elds of mathematics such as algebra, combinatorics, topology, and real analysis. We do not concentrate on the axiomatic framework, although some - pects, such as the axiom of foundation or the role ˆ of the axiom of choice, are elaborated.
690			_aMathematics
942			_2ddc _cPROJECT
999			_c43958 _d43958