An introduction to independence for analysts / H.G. Dales, W.H. Woodin.

Format:

Book

Author/Creator:

Dales, H. G. (Harold G.), 1944- author.

Woodin, W. H. (W. Hugh), author.

Series:

London Mathematical Society lecture note series ; 115.

London Mathematical Society lecture note series ; 115

Language:

English

Subjects (All):

Forcing (Model theory).

Independence (Mathematics).

Axiomatic set theory.

Physical Description:

1 online resource (xiii, 241 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1987.

Language Note:

English

Summary:

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.

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

8.1 DEFINITION

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 229-234) and index.

ISBN:

1-139-88432-8

1-107-36631-3

1-107-37103-1

1-107-36140-0

1-107-37009-4

1-299-40410-3

1-107-36385-3

0-511-66225-4