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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1987.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
115. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Includes indexes. |
| Beschreibung: | 1 online resource (xiii, 241 pages) |
| Bibliographie: | Includes bibliographical references (pages 229-234). |
| ISBN: | 9781107361409 1107361400 9780511662256 0511662254 |
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| 100 | 1 | |a Dales, H. G. |q (Harold G.), |d 1944- |1 https://id.oclc.org/worldcat/entity/E39PCjqV3YmVDTgbYVH3QJMWrC | |
| 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) | ||
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| 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 | |
| 650 | 0 | |a Forcing (Model theory) |0 http://id.loc.gov/authorities/subjects/sh85050461 | |
| 650 | 0 | |a Independence (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85064829 | |
| 650 | 0 | |a Axiomatic set theory. |0 http://id.loc.gov/authorities/subjects/sh85010588 | |
| 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 | |
| 650 | 7 | |a Forcing (Model theory) |2 fast | |
| 650 | 7 | |a Independence (Mathematics) |2 fast | |
| 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) |1 https://id.oclc.org/worldcat/entity/E39PBJdrHdBXMDfgQmMjd8gHYP | |
| 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 |
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| author | Dales, H. G. (Harold G.), 1944- |
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| contents | 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 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 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) 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 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 |
| ctrlnum | (OCoLC)839304847 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839304847 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361409 1107361400 9780511662256 0511662254 |
| language | English |
| oclc_num | 839304847 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 241 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cambridge University Press, |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Dales, H. G. (Harold G.), 1944- https://id.oclc.org/worldcat/entity/E39PCjqV3YmVDTgbYVH3QJMWrC An introduction to independence for analysts / H.G. Dales, W.H. Woodin. Cambridge ; New York : Cambridge University Press, 1987. 1 online resource (xiii, 241 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 115 Includes bibliographical references (pages 229-234). Includes indexes. Print version record. 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. 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 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 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) 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 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 Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Independence (Mathematics) http://id.loc.gov/authorities/subjects/sh85064829 Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Forcing (Théorie des modèles) Indépendance (Mathématiques) Théorie axiomatique des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Forcing (Model theory) fast Independence (Mathematics) fast Verzamelingen (wiskunde) gtt Modeltheorie. gtt Logica. gtt Forcing (théorie des modèles) ram Ensembles, Théorie axiomatique des. ram Woodin, W. H. (W. Hugh) https://id.oclc.org/worldcat/entity/E39PBJdrHdBXMDfgQmMjd8gHYP Print version: Dales, H.G. (Harold G.), 1944- Introduction to independence for analysts. Cambridge ; New York : Cambridge University Press, 1987 0521339960 (DLC) 87021777 (OCoLC)16582061 London Mathematical Society lecture note series ; 115. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552459 Volltext |
| spellingShingle | Dales, H. G. (Harold G.), 1944- An introduction to independence for analysts / London Mathematical Society lecture note series ; 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 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 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) 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 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 Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Independence (Mathematics) http://id.loc.gov/authorities/subjects/sh85064829 Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Forcing (Théorie des modèles) Indépendance (Mathématiques) Théorie axiomatique des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Forcing (Model theory) fast Independence (Mathematics) fast Verzamelingen (wiskunde) gtt Modeltheorie. gtt Logica. gtt Forcing (théorie des modèles) ram Ensembles, Théorie axiomatique des. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85050461 http://id.loc.gov/authorities/subjects/sh85064829 http://id.loc.gov/authorities/subjects/sh85010588 |
| title | An introduction to independence for analysts / |
| title_auth | An introduction to independence for analysts / |
| title_exact_search | An introduction to independence for analysts / |
| title_full | An introduction to independence for analysts / H.G. Dales, W.H. Woodin. |
| title_fullStr | An introduction to independence for analysts / H.G. Dales, W.H. Woodin. |
| title_full_unstemmed | An introduction to independence for analysts / H.G. Dales, W.H. Woodin. |
| title_short | An introduction to independence for analysts / |
| title_sort | introduction to independence for analysts |
| topic | Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Independence (Mathematics) http://id.loc.gov/authorities/subjects/sh85064829 Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Forcing (Théorie des modèles) Indépendance (Mathématiques) Théorie axiomatique des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Forcing (Model theory) fast Independence (Mathematics) fast Verzamelingen (wiskunde) gtt Modeltheorie. gtt Logica. gtt Forcing (théorie des modèles) ram Ensembles, Théorie axiomatique des. ram |
| topic_facet | Forcing (Model theory) Independence (Mathematics) Axiomatic set theory. Forcing (Théorie des modèles) Indépendance (Mathématiques) Théorie axiomatique des ensembles. MATHEMATICS Set Theory. Axiomatic set theory Verzamelingen (wiskunde) Modeltheorie. Logica. Forcing (théorie des modèles) Ensembles, Théorie axiomatique des. |
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