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Set theory: with an introduction to descriptive set theory

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Bibliographic Details
Main Authors:	Kuratowski, Kazimierz 1896-1980 (Author), Mostowski, Andrzej 1913-1975 (Author)
Format:	Book
Language:	English Polish
Published:	Amsterdam [u.a.] North-Holland Publ. Co. [u.a.] 1976
Edition:	2., completely rev. ed.
Series:	Studies in logic and the foundations of mathematics 86
Subjects:	Ensembles, Théorie des Teoria Dos Conjuntos Descriptive set theory Set theory Mengenlehre
Online Access:	Inhaltsverzeichnis
Item Description:	Einheitssacht.: Teoria mnogosci <engl>. - Aus dem Poln. übers.
Physical Description:	514 S.
ISBN:	0720404703

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MARC


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adam_text	CONTENTS Preface to the first edition v Preface to the second edition viii Chapter I. Algebra of sets § 1. Propositional calculus 1 § 2. Sets and operations on sets 4 § 3. Inclusion. Empty set 7 § 4. Laws of union, intersection, and subtraction 10 § 5. Properties of symmetric difference 13 § 6. The set 1, complement 18 § 7. Constituents 21 § 8. Applications of the algebra of sets to topology 27 § 9. Boolean algebras 33 § 10. Lattices 42 Chapter II. Axioms of set theory. Relations. Functions § 1. Set theoretical formulas. Quantifiers 46 § 2. Axioms of set theory 52 § 3. Some simple consequences of the axioms 58 § 4. Cartesian products. Relations 62 § 5. Equivalence relations. Partitions 66 § 6. Functions 69 § 7. Images and inverse images 74 § 8. Functions consistent with a given equivalence relation. Factor Boolean algebras 78 § 9. Order relations 80 § 10. Relational systems, their isomorphisms and types 85 Chapter III. Natural numbers. Finite and infinite sets § 1. Natural numbers 89 § 2. Definitions by induction 93 §3. The mapping / of the set JVxN onto N and related mappings . . 98 § 4. Finite and infinite sets • 102 Xii CONTENTS Chapter IV. Generalized union, intersection and Cartesian product § 1. Set valued functions. Generalized union and intersection 107 § 2. Operations on infinite sequences of sets 117 § 3. Families of sets closed under given operations 121 § 4. T additive and ^ multiplicative families of sets 124 § 5. Reduction and separation properties 127 § 6. Generalized cartesian products 129 § 7. Cartesian products of topological spaces 133 § 8. The Tychonoff theorem 137 § 9. Reduced direct products 140 § 10. Infinite operations in lattices and in Boolean algebras 145 § 11. Extensions of ordered sets to complete lattices 152 § 12. Representation theory for distributive lattices 158 Chapter V. Theory of cardinal numbers § 1. Equipollence. Cardinal numbers 164 § 2. Countable sets 169 § 3. The hierarchy of cardinal numbers 174 § 4. The arithmetic of cardinal numbers 178 § 5. Inequalities between cardinal numbers. The Cantor Bernstein theorem and its generalizations 181 § 6. Properties of the cardinals a and c 188 § 7. The generalized sum of cardinal numbers 191 § 8. The generalized product of cardinal numbers 195 Chapter VI. Linearly ordered sets § 1. Introduction 201 § 2. Dense, scattered, and continuous sets 205 § 3. Order types u, r/, and X 210 § 4. Arithmetic of order types 217 § 5. Lexicographical ordering 220 Chapter VII. Well ordered sets § 1. Definitions. Principle of transfinite induction 224 § 2. Ordinal numbers 228 § 3. Transfinite sequences 230 § 4. Definitions by transfinite induction 233 § 5. Ordinal arithmetic 239 § 6. Ordinal exponentiation 245 § 7. Expansions of ordinal numbers for an arbitrary base 248 § 8. The well ordering theorem 254 § 9. Von Neumann s method of elimination of ordinal numbers . . . 262 CONTENTS Xlii Chapter VIII. Alephs and related topics § 1. Ordinal numbers of power a 267 § 2. The cardinal N(m). Hartogs aleph 270 § 3. Initial ordinals 272 § 4. Alephs and their arithmetic 275 § 5. The exponentiation of alephs 280 § 6. The exponential hierarchy of cardinal numbers 284 § 7. The continuum hypothesis 290 § 8. The number of prime ideals in the algebra P(A) 296 § 9. m disjoint sets 300 § 10. Families of disjoint open sets 302 §11. Equivalence of certain statements about cardinal numbers with the axiom of choice 308 Chapter IX. Trees and partitions § 1. Trees 315 § 2. The lexicographical ordering of zero one sequences. ij{ sets .... 319 § 3. Konig s infinity lemma 326 § 4. Aronszajn s trees 329 § 5. Souslin trees 332 § 6. Some partition theorems 336 Chapter X. Inaccessible cardinals § 1. Normal functions and stationary sets 342 § 2. Weakly and strongly inaccessible cardinals 348 § 3. A digression on models of r°[TR] 352 § 4. Higher types of inaccessible numbers 356 § 5. Weakly compact cardinals 360 § 6. Measurable cardinals 366 § 7. Measurable cardinals and reduced products 375 Incroduction to descriptive set theory Chapter XI. Auxiliary notions § 1. The notion of a metric space. Various fundamental topological notions 386 § 2. Exponential topology. Compact open topology 392 § 3. Complete and Polish spaces 396 § 4. ^. measurable mappings 400 § 5. The operation tf 409 § 6. The Lusin sieve 412 Chapter XII. Borel sets. 5 measurable functions. Baire property § 1. Elementary properties of Borel subsets of a metric space 415 xiv CONTENTS § 2. Ambiguous Borel sets 417 § 3. Borel measurable functions 419 § 4. 5 measurable complex and product functions 421 § 5. Universal functions for Borel classes 423 § 6. Borel subsets of Polish spaces 426 § 7. Further properties of Borel sets 427 § 8. Baire property 428 Chapter XIII. Souslin spaces. Projective sets § 1. Souslin spaces. Fundamental properties 434 § 2. Applications of countable order types to Souslin spaces 444 § 3. Coanalytic sets ^C^ sets) _ 447 § 4. The CT algebra S generated by Souslin sets and the S measurable mappings 451 § 5. The PC^ sets and sets of higher projective classes 455 Chapter XIV. Measurable selectors § 1. The general selector theorem 458 § 2. Selectors for measurable partitions of Polish spaces 463 § 3. Selectors for point inverses of continuous mappings 466 Bibliography 476 List of important symbols 496 Subject index 502
adam_txt	CONTENTS Preface to the first edition v Preface to the second edition viii Chapter I. Algebra of sets § 1. Propositional calculus 1 § 2. Sets and operations on sets 4 § 3. Inclusion. Empty set 7 § 4. Laws of union, intersection, and subtraction 10 § 5. Properties of symmetric difference 13 § 6. The set 1, complement 18 § 7. Constituents 21 § 8. Applications of the algebra of sets to topology 27 § 9. Boolean algebras 33 § 10. Lattices 42 Chapter II. Axioms of set theory. Relations. Functions § 1. Set theoretical formulas. Quantifiers 46 § 2. Axioms of set theory 52 § 3. Some simple consequences of the axioms 58 § 4. Cartesian products. Relations 62 § 5. Equivalence relations. Partitions 66 § 6. Functions 69 § 7. Images and inverse images 74 § 8. Functions consistent with a given equivalence relation. Factor Boolean algebras 78 § 9. Order relations 80 § 10. Relational systems, their isomorphisms and types 85 Chapter III. Natural numbers. Finite and infinite sets § 1. Natural numbers 89 § 2. Definitions by induction 93 §3. The mapping / of the set JVxN onto N and related mappings . . 98 § 4. Finite and infinite sets • 102 Xii CONTENTS Chapter IV. Generalized union, intersection and Cartesian product § 1. Set valued functions. Generalized union and intersection 107 § 2. Operations on infinite sequences of sets 117 § 3. Families of sets closed under given operations 121 § 4. T additive and ^ multiplicative families of sets 124 § 5. Reduction and separation properties 127 § 6. Generalized cartesian products 129 § 7. Cartesian products of topological spaces 133 § 8. The Tychonoff theorem 137 § 9. Reduced direct products 140 § 10. Infinite operations in lattices and in Boolean algebras 145 § 11. Extensions of ordered sets to complete lattices 152 § 12. Representation theory for distributive lattices 158 Chapter V. Theory of cardinal numbers § 1. Equipollence. Cardinal numbers 164 § 2. Countable sets 169 § 3. The hierarchy of cardinal numbers 174 § 4. The arithmetic of cardinal numbers 178 § 5. Inequalities between cardinal numbers. The Cantor Bernstein theorem and its generalizations 181 § 6. Properties of the cardinals a and c 188 § 7. The generalized sum of cardinal numbers 191 § 8. The generalized product of cardinal numbers 195 Chapter VI. Linearly ordered sets § 1. Introduction 201 § 2. Dense, scattered, and continuous sets 205 § 3. Order types u, r/, and X 210 § 4. Arithmetic of order types 217 § 5. Lexicographical ordering 220 Chapter VII. Well ordered sets § 1. Definitions. Principle of transfinite induction 224 § 2. Ordinal numbers 228 § 3. Transfinite sequences 230 § 4. Definitions by transfinite induction 233 § 5. Ordinal arithmetic 239 § 6. Ordinal exponentiation 245 § 7. Expansions of ordinal numbers for an arbitrary base 248 § 8. The well ordering theorem 254 § 9. Von Neumann's method of elimination of ordinal numbers . . . 262 CONTENTS Xlii Chapter VIII. Alephs and related topics § 1. Ordinal numbers of power a 267 § 2. The cardinal N(m). Hartogs' aleph 270 § 3. Initial ordinals 272 § 4. Alephs and their arithmetic 275 § 5. The exponentiation of alephs 280 § 6. The exponential hierarchy of cardinal numbers 284 § 7. The continuum hypothesis 290 § 8. The number of prime ideals in the algebra P(A) 296 § 9. m disjoint sets 300 § 10. Families of disjoint open sets 302 §11. Equivalence of certain statements about cardinal numbers with the axiom of choice 308 Chapter IX. Trees and partitions § 1. Trees 315 § 2. The lexicographical ordering of zero one sequences. ij{ sets . 319 § 3. Konig's infinity lemma 326 § 4. Aronszajn's trees 329 § 5. Souslin trees 332 § 6. Some partition theorems 336 Chapter X. Inaccessible cardinals § 1. Normal functions and stationary sets 342 § 2. Weakly and strongly inaccessible cardinals 348 § 3. A digression on models of r°[TR] 352 § 4. Higher types of inaccessible numbers 356 § 5. Weakly compact cardinals 360 § 6. Measurable cardinals 366 § 7. Measurable cardinals and reduced products 375 Incroduction to descriptive set theory Chapter XI. Auxiliary notions § 1. The notion of a metric space. Various fundamental topological notions 386 § 2. Exponential topology. Compact open topology 392 § 3. Complete and Polish spaces 396 § 4. ^. measurable mappings 400 § 5. The operation tf 409 § 6. The Lusin sieve 412 Chapter XII. Borel sets. 5 measurable functions. Baire property § 1. Elementary properties of Borel subsets of a metric space 415 xiv CONTENTS § 2. Ambiguous Borel sets 417 § 3. Borel measurable functions 419 § 4. 5 measurable complex and product functions 421 § 5. Universal functions for Borel classes 423 § 6. Borel subsets of Polish spaces 426 § 7. Further properties of Borel sets 427 § 8. Baire property 428 Chapter XIII. Souslin spaces. Projective sets § 1. Souslin spaces. Fundamental properties 434 § 2. Applications of countable order types to Souslin spaces 444 § 3. Coanalytic sets ^C^ sets) _ 447 § 4. The CT algebra S generated by Souslin sets and the S measurable mappings 451 § 5. The PC^ sets and sets of higher projective classes 455 Chapter XIV. Measurable selectors § 1. The general selector theorem 458 § 2. Selectors for measurable partitions of Polish spaces 463 § 3. Selectors for point inverses of continuous mappings 466 Bibliography 476 List of important symbols 496 Subject index 502
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author	Kuratowski, Kazimierz 1896-1980 Mostowski, Andrzej 1913-1975
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spelling	Kuratowski, Kazimierz 1896-1980 Verfasser (DE-588)107876779 aut Set theory with an introduction to descriptive set theory 2., completely rev. ed. Amsterdam [u.a.] North-Holland Publ. Co. [u.a.] 1976 514 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics 86 Einheitssacht.: Teoria mnogosci <engl>. - Aus dem Poln. übers. Ensembles, Théorie des Teoria Dos Conjuntos larpcal Descriptive set theory Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 Mostowski, Andrzej 1913-1975 Verfasser (DE-588)118584510 aut Studies in logic and the foundations of mathematics 86 (DE-604)BV000893472 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015338284&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kuratowski, Kazimierz 1896-1980 Mostowski, Andrzej 1913-1975 Set theory with an introduction to descriptive set theory Studies in logic and the foundations of mathematics Ensembles, Théorie des Teoria Dos Conjuntos larpcal Descriptive set theory Set theory Mengenlehre (DE-588)4074715-3 gnd
subject_GND	(DE-588)4074715-3
title	Set theory with an introduction to descriptive set theory
title_auth	Set theory with an introduction to descriptive set theory
title_exact_search	Set theory with an introduction to descriptive set theory
title_exact_search_txtP	Set theory with an introduction to descriptive set theory
title_full	Set theory with an introduction to descriptive set theory
title_fullStr	Set theory with an introduction to descriptive set theory
title_full_unstemmed	Set theory with an introduction to descriptive set theory
title_short	Set theory
title_sort	set theory with an introduction to descriptive set theory
title_sub	with an introduction to descriptive set theory
topic	Ensembles, Théorie des Teoria Dos Conjuntos larpcal Descriptive set theory Set theory Mengenlehre (DE-588)4074715-3 gnd
topic_facet	Ensembles, Théorie des Teoria Dos Conjuntos Descriptive set theory Set theory Mengenlehre
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015338284&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000893472
work_keys_str_mv	AT kuratowskikazimierz settheorywithanintroductiontodescriptivesettheory AT mostowskiandrzej settheorywithanintroductiontodescriptivesettheory

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