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An introduction to independence for analysts /
Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a nat...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1987.
|
| Colección: | London Mathematical Society lecture note series ;
115. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
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| 008 | 130415s1987 enk ob 001 0 eng d | ||
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| 100 | 1 | |a Dales, H. G. |q (Harold G.), |d 1944- | |
| 245 | 1 | 3 | |a An introduction to independence for analysts / |c H.G. Dales, W.H. Woodin. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1987. | ||
| 300 | |a 1 online resource (xiii, 241 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 115 | |
| 504 | |a Includes bibliographical references (pages 229-234). | ||
| 500 | |a Includes indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; 1 HOMOMORPHISMS FROM ALGEBRAS OF CONTINUOUS FUNCTIONS; 1.1 DEFINITION; 1.2 THEOREM; 1.3 THEOREM; 1.4 DEFINITION; 1.5 DEFINITION; 1.6 THEOREM; 1.7 COROLLARY; 1.8 THEOREM; 1.9 THEOREM (CH); 1.10 THEOREM (CH); 1.11 THEOREM (CH); 1.12 THEOREM (CH); 1.13 THEOREM; 1.14 NOTES; 2 PARTIAL ORDERS, BOOLEAN ALGEBRAS, AND ULTRAPRODUCTS; 2.1 DEFINITION; 2.2 EXAMPLES; 2.3 DEFINITION; 2.4 PROPOSITION; 2.5 DEFINITION; 2.6 DEFINITION; 2.7 EXAMPLE; 2.8 DEFINITION; 2.9 DEFINITION; 2.10 THEOREM; 2.11 DEFINITION; 2.12 DEFINITION; 2.13 LEMMA; 2.14 THEOREM; 2.15 COROLLARY | |
| 505 | 8 | |a 2.16 EXAMPLE2.17 DEFINITION; 2.18 DEFINITION; 2.19 DEFINITION; 2.20 THEOREM; 2.21 THEOREM; 2.22 DEFINITION; 2i23 DEFINITION; 2.24 THEOREM; 2.25 NOTES; 3 WOODIN'S CONDITION; 3.1 DEFINITION; 3.2 THEOREM; 3.3 THEOREM; 3.4 PROPOSITION; 3.5 DEFINITION; 3.6 PROPOSITION; 3.7 PROPOSITION; 3.8 NOTES; 4 INDEPENDENCE IN SET THEORY; 4.1 DEFINITION; 4.2 DEFINITION; 4.3 DEFINITION; 4.4 DEFINITION; 4.5 DEFINITION; 4.6 DEFINITION; 4.7 DEFINITION; 4.8 THEOREM; 4.9 DEFINITION; 4.10 EXAMPLES; 4.11 DEFINITION; 4.12 DEFINITION; 4.13 DEFINITION; 4.14 DEFINITION; 4.15 EXAMPLE; 4.16 THEOREM; 4.17 THEOREM | |
| 505 | 8 | |a 4.18 DEFINITION4.19 THEOREM; 4.20 NOTES; 5 MARTIN'S AXIOM; 5.1 DEFINITION; 5.2 DEFINITION; 5.3 DEFINITION; 5.4 PROPOSITION; 5.5 DEFINITION; 5.6 DEFINITION; 5.7 PROPOSITION; 5.8 DEFINITION; 5.9 PROPOSITION; 5.10 DEFINITION; 5.11 PROPOSITION (; 5.12 THEOREM; 5.13 DEFINITION; 5.14 DEFINITION; 5.15 DEFINITION; 5.16 LEMMA; 5.17 DEFINITION; 5.18 LEMMA; 5.19 LEMMA; prefilter in P, and hence, by 2.9(ii), H is a filter. I5.20 THEOREM; 5.21 DEFINITION; 5.22 THEOREM (MA); 5.23 DEFINITION; 5.24 THEOREM; 5.25 THEOREM (MA); 5.26 THEOREM (MA); 5.27 COROLLARY (MA); 5.28 COROLLARY; 5.29 THEOREM (MA) | |
| 505 | 8 | |a 5.30 NOTES6 GAPS IN ORDERED SETS; 6.1 PROPOSITION; 6.2 COROLLARY; 6.2 DEFINITION; 6.4 DEFINITION; 6.5 DEFINITION; 6.6 PROPOSITION; 6.7 DEFINITION; 6.8 PROPOSITION; 6.9 THEOREM (MA + iCH); 6.10 DEFINITION; 6.11 DEFINITION; 6.12 THEOREM; 6.13 THEOREM; 6.14 COROLLARY (MA + *1CH); 6.15 THEOREM (MA); 6.16 THEOREM (MA); 6.17 DEFINITION; 6.18 PROPOSITION; 6.19 COROLLARY; 6.20 DEFINITION; 6.21 DEFINITION; 6.22 PROPOSITION; 6.23 PREPOSITION; 6.24 THEOREM (MA + nCH); 6.25 THEOREM (MA + iCH); 6.2 6 PROPOSITION; 6.27 COROLLARY; 6.28 COROLLARY (MA + nCH); 6.30 NOTES; 7 FORCING; 7.1 DEFINITION; 7.2 EXAMPLE | |
| 505 | 8 | |a 7.3 DEFINITION7.4 PROPOSITION; 7.5 PROPOSITION; 7.6 DEFINITION; 7.7 DEFINITION; 7.8 PROPOSITION; 7.9 PROPOSITION; 7.10 LEMMA; 7.11 PROPOSITION; 7.12 THEOREM; 7.13 METATHEOREM; 7.14 EXAMPLE; 7.15 THEOREM; 7.16 PROPOSITION; 7.17 DEFINITION; 7.18 LEMMA; 7.19 LEMMA; 7.20 LEMMA; 7.21 LEMMA; 7.22 LEMMA; 7.23 DEFINITION; 7.24 EXAMPLE; 7.25 DEFINITION; 7.26 THEOREM; 7.27 THEOREM; 7.28 THEOREM; 7.29 COROLLARY (CH); 7.30 THEOREM; 7.31 DEFINITION; 7.32 PROPOSITION; 7.33 THEOREM; 7.34 THEOREM; 7.35 DEFINITION; 7.36 LEMMA; 7.37 THEOREM; 7.40 DEFINITION; 7.41 THEOREM; 7.42 NOTES; 8 ITERATED FORCING | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Forcing (Model theory) | |
| 650 | 0 | |a Independence (Mathematics) | |
| 650 | 0 | |a Axiomatic set theory. | |
| 650 | 6 | |a Forcing (Théorie des modèles) | |
| 650 | 6 | |a Indépendance (Mathématiques) | |
| 650 | 6 | |a Théorie axiomatique des ensembles. | |
| 650 | 7 | |a MATHEMATICS |x Set Theory. |2 bisacsh | |
| 650 | 7 | |a Axiomatic set theory. |2 fast |0 (OCoLC)fst00824491 | |
| 650 | 7 | |a Forcing (Model theory) |2 fast |0 (OCoLC)fst00931616 | |
| 650 | 7 | |a Independence (Mathematics) |2 fast |0 (OCoLC)fst00968877 | |
| 650 | 1 | 7 | |a Verzamelingen (wiskunde) |2 gtt |
| 650 | 1 | 7 | |a Modeltheorie. |2 gtt |
| 650 | 1 | 7 | |a Logica. |2 gtt |
| 650 | 7 | |a Forcing (théorie des modèles) |2 ram | |
| 650 | 7 | |a Ensembles, Théorie axiomatique des. |2 ram | |
| 700 | 1 | |a Woodin, W. H. |q (W. Hugh) | |
| 776 | 0 | 8 | |i Print version: |a Dales, H.G. (Harold G.), 1944- |t Introduction to independence for analysts. |d Cambridge ; New York : Cambridge University Press, 1987 |z 0521339960 |w (DLC) 87021777 |w (OCoLC)16582061 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 115. | |
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