Description |
1 online resource (xi, 236 pages). |
Physical Medium |
polychrome |
Description |
text file |
Series |
London Mathematical Society student texts ; 39
|
|
London Mathematical Society student texts ; 39.
|
Bibliography |
Includes bibliographical references (pages 225-227) and index. |
Contents |
Basics of set theory -- Axiomatic set theory -- Why axiomatic set theory? -- Language and the basic axioms -- Relations, functions, and Cartesian product -- Relations and the axiom of choice -- Functions and the replacement scheme axiom -- Generalized union, intersection, and Cartesian product -- Partial- and linear-order relations -- Natural numbers, integers, and real numbers -- Natural numbers -- Integers and rational numbers -- Real numbers -- Fundamental tools of set theory -- Well orderings and transfinite induction -- Well-ordered sets and the axiom of foundation -- Ordinal numbers -- Definitions by transfinite induction -- Zorn's lemma in algebra, analysis, and topology -- Cardinal numbers -- Cardinal numbers and the continuum hypothesis -- Cardinal arithmetic -- Cofinality -- Power of recursive definitions -- Subsets of R[superscript n] -- Strange subsets of R[superscript n] and the diagonalization argument -- Closed sets and Borel sets -- Lebesgue-measurable sets and sets with the Baire property -- Strange real functions -- Measurable and nonmeasurable functions -- Darboux functions -- Additive functions and Hamel bases -- Symmetrically discontinuous functions -- When induction is too short -- Martin's axiom -- Rasiowa-Sikorski lemma -- Martin's axiom -- Suslin hypothesis and diamond principle -- Forcing -- Elements of logic and other forcing preliminaries -- Forcing method and a model for [not sign]CH -- Model for CH and [diamonds suit symbol] -- Product lemma and Cohen model -- Model for MA+[not sign]CH. |
Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
Subject |
Set theory.
|
|
Set theory. |
Genre/Form |
Electronic books.
|
Other Form: |
Print version: Ciesielski, Krzysztof, 1957- Set theory for the working mathematician. Cambridge ; New York : Cambridge University Press, ©1997 0521594413 (DLC) 97010533 (OCoLC)36621835 |
ISBN |
9781139173131 (electronic book) |
|
1139173138 (electronic book) |
|
9781107089068 (electronic book) |
|
1107089069 (electronic book) |
|
0521594413 |
|
9780521594417 |
|
0521594650 |
|
9780521594653 |
|